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

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 μm/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 Hunt–Crossley model and a modified linear Kelvin–Voigt model were used to predict the dynamic response with set mass and shape coefficient parameters. The Hunt–Crossley model predicted well both the maximum force and maximum deflection for each ball type. The Hunt–Crossley 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 Kelvin–Voigt model and experimental contact times was 7.6%, while the corresponding mean difference for the coefficient of restitution was 13.1%. Overall, the modified Kelvin–Voigt 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.

► New impact models to describe dynamic collision responses of balls were developed.
► Only the few fitted model constants of stiffness, κ, and damping, λ, are required.
► Non-linear model stiffness was shown to be related to static Hertzian stiffness.
► A corresponding linear impact model was derived from the Hunt–Crossley model.
► Impact velocity is more important in determining response compared to ball core type.