A Critical Study of the Applicability of Rigid-Body Collision Theory

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Abstract
This article deals with the collision of steel bars with external surfaces. The central issue of the article is the investigation of the fundamental concepts that are used to solve collision problems by using rigid-body theory. We particularly focus on low-velocity impacts of relatively rigid steel bars to test the applicability of these concepts. An experimental analysis was conducted to study the rebound velocities of freely dropped bars on a large external surface. A high-speed video system was used to capture the kinematic data. The number of contacts and the contact time were determined by using an electrical circuit and an oscilloscope. Tests were performed by using six bar lengths and varying the pre-impact inclinations and the velocities of the bars. The experimental results were used to verify the applicability of Coulomb’s law of friction and the invariance of the coefficient of restitution in the class of impacts considered in this study. Then, given the unusual variation the coefficient of restitution as a result of changing pre-impact inclinations, a theoretical model was developed to explain this variation. A discrete model of the bar was used to obtain the equations of motion during impact. Computed and experimental results were compared to establish the accuracy of numerical model. The internal vibrations of the bar and multi impacts between the bar and the surface were found to be two main factors that cause the variation of the coefficient of restitution. Furthermore, a slenderness factor was proposed to identify the subset of collision problems where the coefficient of restitution was invariant to the inclination angle.

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