Comprehensive analyses of the elasto-plastic oblique contact-impact with vibration response

Contact-impact between different surfaces is a ubiquitous phenomenon especially in the mechanical systems. Previous work of authors indicated that the effect of longitudinal and/or transverse vibration response during the motion and dynamic modeling cannot be neglected for the elasto-plastic contact-impact events. In this study, further analyses were performed to characterize the contribution of longitudinal and transverse vibration responses during the elasto-plastic oblique contact-impact, and the formula to calculate the influence factor of vibration, ξ, was proposed based on the contact force with different vibrations during the impact. The momentum theorem and assumed mode method were used to develop the equations of motion of a flexible bar with a solid flat surface. Simulation results were compared with experimental results reported in the literature to verify the accuracy of the established model. The tangential and normal velocities of the contact point after the impact were compared with the simulations for different vibration cases, and the comparison between the simulations and the experimental results had yield encourage results. For different elasto-plastic materials, three critical initial impact angles had been found from the simulation to determine whether the flexible bar slides or sticks the flat surface. Although considering the effect of vibration response during the motion and dynamic modeling is very significant, increasing the number of shape functions did not effect the result significantly. The longitudinal and transverse vibration responses were found to effect the normal and tangential velocities of the contact point after the impact, respectively. Moreover, it had been shown that for the oblique contact-impact with sliding, considering the response of longitudinal and transverse vibration at the same time is more reasonable than other cases, which also reveals that, in this case, there is a good agreement between the simulation and experimental results. Besides, the mathematical expression on the influence factor of vibration depending on the initial velocity also had been obtained by a numerical analysis. This work can provide useful insights for dynamic modeling of complex multi-body systems during the contact-impact.