Simulation of the impact response of a sliotar core with linear and non-linear contact models

Abstract

Static and dynamic models of the characteristic responses of sliotar cores made of both cork and polyurethane were studied in this work in order to understand their constitutive behaviour. Data from quasi-static tests at 10 mm/s and from dynamic impacts at speeds from 5 to 25 m/s were used to develop and evaluate the models. The quasi-static response was described well by Hertzian theory. A non-linear HunteCrossley model and a modified linear KelvineVoigt model were used to predict the dynamic response with set mass and shape coefficient parameters. The HunteCrossley model predicted well both the maximum force and maximum deflection for each ball type. The HunteCrossley model generally captured the experimental contact times well with a mean difference between experimental and model contact times of 8.3%. The mean difference between the KelvineVoigt model and experimental contact times was 7.6%, while the corresponding mean difference for the coefficient of restitution was 13.1%. Overall, the modified KelvineVoigt model predicted the parameters of contact time and coefficient of restitution well. Contact time and coefficient of restitution prediction in this linear model were not particularly sensitive to the strain rate.

A Contact Force Model With Nonlinear Compliance and Residual Indentation1

“…The Hunt-Crossley (HC) model [12] is another compliant contact model that is free from such weaknesses. [1,2,8,[19][20][21]. This model is extended in Refs.…”

“…The behaviors of the state variable a is defined by the ODE (8a) and the force/ is determined by the output equation (8è). Equation (8) implies that, in the model (7), the force/ is always nonnegative and continuous with respect to p and a. Equation (8) implies that, in the model (7), the force/ is always nonnegative and continuous with respect to p and a.…”

“…A great amount of effort has been focused upon the modeling of contact, especially among biological tissues [1,2], components of machinery [3,4], rubber materials [5][6][7][8], and granular materials [9,10]. The force exerted by a contact varies according to nonlinear relations with time and the relative displacement, both during the contact and at the beginning and end of the contact.…”

Articular Contact Mechanics

“…Other approximate relations connecting the damping parameter b and the coefficient of restitution e * are discussed in [37,43,71,82,89] along with the applications of the Hunt-Crossley model in multibody dynamics simulations. Observe that the coefficient of restitution in the linear viscoelastic impact models [9,73] depends on the impactor mass and does not depend on the impact velocity.…”

“…Otherwise, we suggest a simple approximation ω = π/(2t m ), where t m is a characteristic time period of the loading phase up to the moment of peak contact approach. As in [37,43,71], the parameter v 0 in formula (7.80) is interpreted as the initial contact velocity.…”