Contact time at impact of spheres on large thin plates

Abstract

Using a free-fall apparatus, the low-velocity impact behavior of steel spheres impacting on large thin glass plates had been experimentally measured. The impact and rebound velocities had been determined from the time interval between consecutive impacts and thereby the coefficient of restitution (CoR) had been evaluated. The contact time had been measured from the transmitted current during contact of the sphere (soldered with a very thin flexible conductive wire) and the plate (coated with a thin conductive layer) when a closed circuit is created. The influences of the impact velocity, the sphere size and the plate thickness on the impact behavior had been investigated.The measurement values had been compared with the theoretical predictions of the Hertz and the Zener models. Thereby, a detailed discussion is presented about the inadequacy of the Hertz model to accurately predict the contact time (in comparison to the better applicable Zener model) for a sphere impacting on an infinitely extended elastic plate of finite thickness, where longitudinal and transversal waves can propagate and travel several times (below the contact area) through the plate within the contact time whereby flexural waves arise. Similarly, the limitations of the Zener model such as the overestimations of the CoR (due of negligence of energy dissipation by friction and viscous damping) are also illustrated with help of experimental results and thereby, the effective limits of reliability of the Zener model are discussed considering the underestimations of the contact time for thin plates.