Coefficient of Restitution Interpreted as Damping in Vibroimpact

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 λxnx˙ 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.

On the continuous contact force models for soft materials in multibody dynamics

“…Hunt and Crossley [31] showed that the linear spring-damper model does not represent the physical nature of energy transferred during the contact. Instead, they represented the contact force by the Hertz force-deformation law with a nonlinear viscous-elastic element as…”

“…Based on the analysis of Hunt and Crossley [31] that separates the contact force into elastic and dissipative components, the force model proposed by Lankarani and Nikravesh can be expressed as…”

“…First of all, part of the initial kinetic energy is transformed into elastic strain energy which, in turn, is converted in the final kinetic energy at the end of the contact. The remaining amount of kinetic energy is dissipated during the contact process in several forms such as wave propagation [8,30], material damping [4,31], plasticity [5,32], and heat [23,33]. Stronge [8] demonstrated that stress and deformation waves do not contribute to energy dissipation when the size and material properties of the contacting bodies are similar.…”

Enhanced chain dynamics in loop-sorting-systems by means of layout optimization and a kinematic model of the polygon action

“…To search the wheel contact, a kinematic formulation of the track layout is utilized assuming the track to be rigid and all track sections to by perfectly aligned and tangent to each other. The wheel and joint contacts are modeled using the continuous Hunt-Crossly formulation in which the contact force are computed by the indentation and the indentation velocity between the intersecting bodies, see Hunt and Crossley (1975). The motor force is applied as a point force onto the bottom of all carts located above a linear motor.…”

Load assessment and analysis of impacts in multibody systems

“…A significant number of such force models is available (e.g. [10], [12], [7], [19]). These are often based on the assumption of Hertzian contact together with various representations for dissipation.…”