Effect of pre-impact waves in an elastic rod on coefficient of restitution

B Lundberg,T Rastemo,J Huo

doi:10.1016/j.ijimpeng.2021.103816

Abstract

The effect of pre-impact waves on the coefficient of restitution (COR) in longitudinal impact of a uniform elastic rod on a linear elastic or bilinear inelastic spring supported by a fix rigid wall is studied. The spring models may represent the quasi-static response of, e.g., a small elastic cylinder or the inelastic bit-rock interaction in percussive drilling. The rod is accelerated to its impact momentum either by a force of relatively short duration which generates significant pre-impact waves in the rod (pre-impact wave case) or by a force of long duration which does not generate such waves (reference case). Analytical and numerical results based on the 1D wave equation are presented in dimensionless form. It is shown that the work performed by the accelerating force is much larger in the pre-impact wave case than in the reference case, and that the COR generally depends on spring stiffness, elasticity parameter, initial rod-spring separation, and wave transit time. In the pre-impact wave case, the COR may be significantly larger or smaller than in the reference case. It may also be significantly larger or smaller than unity. A pre-impact wave mechanism leading to super rebounds with COR up to 1.4261 is described.

Highlights

A force accelerating an elastic body to its momentum at impact generates pre-impact elastic waves in the body
The effect of pre-impact waves on the coefficient of restitution (COR) in longitudinal impact of a uniform elastic rod on a linear elastic or bilinear inelastic spring supported by a fix rigid wall has been studied
Significant pre-impact waves are generated by a force accelerating the rod to its impact momentum if the force has short duration relative to the wave transit time

Summary

Introduction

A force accelerating an elastic body to its momentum at impact generates pre-impact elastic waves in the body. Pre-impact waves are significant in slender bodies such as rods that are accelerated in their longitudinal direction by forces of relatively short duration. Under such conditions, the following questions related to the effect of pre-impact waves on the coefficient of restitution (COR) are of interest: (i) What is the effect of such waves on the COR? A cylindrical rod with indenters at its front end is hit axially at its rear end by a hammer This produces an accelerating force on the drill rod towards the rock, commonly with duration much shorter than the wave transit time. Recent reviews of literature have been provided by Khulief [11] and Ahmad et al [12], and exten sive text books have been written by Goldsmith [13], Johnson [14] and Stronge [15]

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