Low and high speed impacts frequently occur in many mechanical processes. Although widely studied, rarely are normal and tangential force time-waveforms measured, as generally these are very difficult measurements to do accurately. This paper presents, for the first time, a comprehensive set of experimentally obtained contact force waveforms during oblique elastic impact for a range of initial velocities and incidence angles. The experimental apparatus employed in this study was a simple pendulum consisting of a spherical steel striker suspended from a steel wire. The contact force time-waveforms were collected using a tri-axial piezoelectric force transducer sandwiched between a spherical target cap and a large block. The measured contact forces showed that loading was essentially limited to the normal and tangential directions in the horizontal plane. Analysis of the maximum normal and tangential forces for the near glancing angles of incidence indicated a friction coefficient that varies linearly with initial tangential velocity. The essential features of tangential force reversal during impact predicted by previous continuum models are confirmed by the experimental force results.
A new solution method for the oblique elastic impact of similar spheres with Coulomb friction is presented. The solution uses approximations of the shear stress distributions at each time step during impact. These distributions are solved from analytical formulations and are able to account for both full sliding and partial-slip scenarios that may both be present for this problem due to inclusion of tangential compliance and friction effects. Comparison to previous continuum models in the literature shows very good agreement for the contact force wave forms obtained. The major advantage of this method is the drastic reduction in computation time required compared to previous solutions.
Applied dynamic loads are often difficult to measure accurately due to the dynamic response of the sensor used and the dependence of the sensor's sensitivity on the mounting and loading details. For tri-axial force transducers, which are capable of measuring forces along the axial direction and along both directions of the transducer's face, dynamic calibration is further complicated by the coupling of the sensor's measurement directions. For this reason, a new apparatus for dynamic calibration of normal and tangential directions of a tri-axial piezoelectric force transducer has been constructed and tested. The calibration force is provided from a spring loaded uni-axial impulse hammer. The apparatus allows for calibration at a variety of calibration angles and speeds; the loading for all cases of a nonzero calibration angle is oblique, with the point of force application being eccentric to the centerline of the force transducer's normal axis. As such, tangential loads are always accompanied by a normal load. The calibration results show that the normal direction correction factors have a systematic dependence on the calibration angle; the tangential correction factors show some scatter but do not appear to be dependent on the calibration angle.
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