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Abstract
This paper is concerned with the modeling and simulation of two- and three-dimensional impact in the presence of friction. Single impacts are considered, and the impact equations are solved algebraically. Impact generates impulsive normal and frictional forces and the direction of sliding can change during impact. A procedure is developed to estimate the change in direction of sliding during three-dimensional impact. The modes of impact, such as sliding, sticking, or change in direction of sliding, are classified for both two- and three-dimensional impact. Simulations are conducted to analyze the energy lost, change in impact direction, and stick-slip conditions, where different models for restitution are compared. A closed-form solution is developed to analyze the modes of sliding for two-dimensional impact.
Highlights
Research about impact between two rigid bodies spans centuries
Post-impact parameters are analyzed for three-dimensional impact
It is observed that the three-dimensional results follow closely from two-dimensional impact results, with more sliding observed for three-dimensional impact
Summary
Research about impact between two rigid bodies spans centuries. There are two fundamental parameters that dictate how impact takes place: coefficient of restitution and coefficient of friction. Restitution modeling was considered before friction modeling, with Poisson’s and Newton’s models used to model restitution. Poisson’s model is kinetic and defines the coefficient of restitution by the ratio of the normal forces before and after impact while Newton’s method is kinematic and considers velocity ratios. The two approaches lead to the same result, as shown by Wang and Mason [1]. They can produce inconsistent results, especially in the presence of friction, as shown by Stronge [2]. Routh [3] presented a graphic method to define the coefficient of restitution
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