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Abstract
This thesis deals with the special case of low velocity oblique elastic impact of bodies with circular contact zones. This special case of impact is of particular interest in the simulation of tube-support interaction, robotics and granular assemblies, and can be associated with fretting wear; the results obtained can be extended to cylindrical impact. This study focuses on the characterization of the shear stress distributions and tangential contact forces during oblique impact. The study includes theoretical and computational modeling, as well as experimental investigations.
The theoretical model presented in this study uses analytical approximations to find the unknown shear stress distributions at each time step; these shear stresses are then used to find the tangential forces. The approach used results in a more direct method of solution while attaining a nearly identical solution for the tangential force waveforms.
The developed finite element model, which utilized a penalty contact formulation with explicit dynamic time stepping using Abaqus™/Explicit software, resulted in unexpected transient spikes in values of both the normal and shear stress distributions throughout the impact duration. The shear stress distributions also show unexpected antisymmetry in both the x-axis (loading) and y-axis (perpendicular to loading) directions. Despite these unexpected behaviours, the finite element model displayed tangential force oscillation similar to that predicted by the continuum model.
The experimental force waveforms, obtained using a simple pendulum apparatus with a triaxial piezoelectric force transducer, showed good repeatability over the range of incidence angles and initial velocities considered. Loading was essentially limited to the normal and horizontal directions. Oscillation of the experimentally obtained horizontal force waveforms occurred over the approximate range of incidence angles predicted by theory. Post impact ringing, caused by mounting block natural frequency response, of the horizontal force waveforms was more significant than in the normal force waveform. This caused apparent friction envelope violation towards the end of impact of the normalized horizontal force waveforms. Analysis of the experimental force waveforms indicated that a friction model that varied linearly with initial tangential velocity was more appropriate than a constant coefficient of friction. These friction models were also dependent on the overall initial velocity. When these friction models were implemented in the continuum model, the results obtained showed reasonable agreement with the experiments.
In conclusion, the essential features of tangential force oscillation predicted by the continuum model were present in the finite element model results and the experimentally obtained force waveforms. In general, the continuum model predicted earlier tangential force reversal time and higher magnitude minimum tangential forces than either the finite element results or experimentally obtained waveforms. The change in normal direction momentum, as judged by terminal impulse values, indicated that damping may have a small but significant effect in the experimental normal force results. Neither the continuum model nor the finite element model included damping effects.
