Comparisons of Contact Forces during Oblique Impact: Experimental vs. Continuum and Finite Element Results

Abstract

Low speed oblique impacts are commonly encountered in many areas of engineering interest such as machinery operation, robotics, granular flow, and tube/support interactions. Although it is a fundamental topic in introductory mechanics, oblique impact presents many difficulties due in particular to the complex interaction of compliance and friction that is expected to occur in the tangential direction at the contact surface. The compliance and friction interaction can, theoretically, lead to different scenarios whereby coincident points in the shared contact zone of the two bodies all have no relative slip (i.e., full sticking), all have some relative slip (i.e., full sliding) or are split between an inner portion that is sticking with an outer portion that is slipping (i.e., partial-slip). The situation is believed to be responsible for some rather interesting tangential contact force waveforms, and, in particular, leads to possible tangential force direction reversal within the impact duration for near normal angles of incidence. Many questions regarding oblique impact have yet to be answered conclusively.In this paper, comparisons of contact force results obtained from continuum and finite element models of oblique elastic impact are made to the authors’ previously published experimental results for steel-on-steel impact. Also included are the comparison of rebound angles and impulse ratios. The continuum model is purely elastic with no damping while the finite element model is elastic but contains a small amount of numerical damping. The impact force waveform comparisons show very reasonable agreement between both simulations and experiments, with the essential features of tangential force reversal being present in all three sets of results. The major source of difference in the normal force waveform results is believed to be a small amount of energy dissipation that is present in the experimental results but is largely unaccounted for in these models. Given the low speeds employed in the experiments, this dissipation is not believed to be related to plastic deformation. For the tangential force waveforms, the differences in the results are believed to be mainly due to slight contamination of the experimental data by natural frequency response of the measurement setup. The impulse ratio results comparisons show reasonable agreement among the methods while the rebound angle agreement is less encouraging. This indicates that the rebound angle is somewhat more sensitive to certain differences among the sets of results. While the finite element simulations required many hours of computation, the continuum model provided shear stress distributions and force waveforms in seconds.