Frictional Impact Analysis in Open-Loop Multibody Mechanical Systems

Abstract

Analysis of impact problems in the presence of any tangential component of impact velocity requires a friction model capable of correct detection of the impact modes. This paper presents a formulation for the analysis of impact problems with friction in open-loop multibody mechanical systems. The formulation recognizes the correct mode of impact; i.e., sliding, sticking, and reverse sliding. Poisson’s hypothesis is used for the definition of the coefficient of restitution, and thus the energy gains inherent with the use of the Newton’s hypothesis are avoided. The formulation is developed by using a canonical form of the system equations of motion using joint coordinates and joint momenta. The canonical momentum-balance equations are solved for the change in joint momenta using Routh’s graphical method. The velocity jumps are calculated balancing the accumulated momenta of the system during the impact process. The impact cases are classified based on the pre-impact positions and velocities, and inertia properties of the impacting systems, and expressions for the normal and tangential impulse are derived for each impact case. The classical problem of impact of a falling rod with the ground (a single object impact) is solved with the developed formulation and verified. Another classical problem of a double pendulum striking the ground (a multibody system impact) is also presented. The results obtained for the double pendulum problem confirms that the energy gain in impact analysis can be avoided by considering the correct mode of impact and using the Poisson’s instead of the Newton’s hypothesis.