Laboratory investigation of the effect of the rotational speed on the coefficient of restitution

Abstract

In the process of impact-rebound, rockfalls with an initial rotational speed (RS) often undergo a violent transformation between rotational energy and translational energy, which may affect the coefficient of restitution (COR). However, owing to the complexity of experimental simulations and the influence mechanism, this issue is often neglected during research. Therefore, in this study, four representative blocks (ellipsoid, cylinder, cone with a spherical base, and disc) were selected, and impact tests of each block rotating around different axes with various RSs were conducted using a specially developed device. Based on the impact dynamics theory, the RS has no significant effect on the tangential COR (Rt), while it may exhibit a positive correlation with the Rt when the size of the block size is large enough. When the block rotates around the X-axis (approximately normal impact), there is no obvious relationship between the RS and the normal COR (Rn). Conversely, when the block rotates around the Y-axis (often non-normal impact), the RS influences the Rn, but it is difficult to determine in what manner and to what extent. Thus, to clarify the influence mechanism of RS on the Rn for non-normal impacts, a comprehensive variable, the impact posture coefficient (IPC), which comprehensively considers the RS, block shape, and impact posture, was introduced, and the impact-rebound characteristics of the blocks were classified and discussed. Under the condition of bouncing after only one impact, the IPC and Rn values exhibited a positive linear correlation when the block mass centre (C) is behind the contact point (CP), whereas the opposite behaviour was observed when the C is in front of the CP. Meanwhile, under the condition of bouncing after two impacts, the Rn and IPC values had a positive linear correlation. These findings explain the influence mechanism of RS on the COR and provide a new idea for the accurate prediction of the impact-rebound processes of rotating irregular rockfalls.