A novel approach to evaluate the elastic impact of spheres on thin plates. (22nd December 2015) - Mueller, Peter; Boettcher, Ronny; Russell, Alexander; Truee, Michael; Tomas, Juergen
Abstract: A novel analytical approach to solve the otherwise mathematically strenuous Zener model for elastic sphere impacts on large, thin plates, has been presented to find a comfortable solution for the coefficient of restitution (CoR). The proposed analytical approach provides accurate results for the range of coefficients of restitution larger than 0.2 and gives a very good approximation of the Zener model. Furthermore, the Zener model has been numerical solved with high accuracy and has been used to evaluate the inelasticity parameter as well as the coefficient of restitution for different material combinations and ratios of sphere diameter to plate thickness. Both approaches have been used to evaluate the coefficient of restitution of elastic glass beads at impact with glass plates of different thicknesses using experimental free fall test measurements. A significant dependence of the coefficient of restitution of elastic spheres on the ratio of sphere diameter to plate thickness as well as on the impact velocity and on the inelasticity parameter has been observed respectively, which can be well described by the Zener model and the proposed analytical approach. Graphical abstract: Highlights: Description of Zener׳s approach to evaluate impact energy characteristics. Derivation of a Zener model based simple analytical approach for the CoR. Evaluation of the influence of the ratio of sphere diameter to plate thickness. Determination of the influence of impact velocity on the CoR.