Rigid Body Impact Modeling Using Integral Formulation

[+] Author and Article Information
Yuning Zhang

Department of Mechanical Engineering, McGill University, Montreal, Quebec, H3A 2K6, Canadayuning.zhang@mail.mcgill.ca

Inna Sharf

Department of Mechanical Engineering, McGill University, Montreal, Quebec, H3A 2K6, Canadainna.sharf@mcgill.ca

Note, in Keller’s original work, uT is expressed with only the two components in the contact plane, the third component being identically zero.

J. Comput. Nonlinear Dynam 2(1), 98-102 (Sep 10, 2006) (5 pages) doi:10.1115/1.2389232 History: Received May 12, 2006; Revised September 10, 2006

A three-dimensional single-point impact solution has been developed based on the original work of Keller. The formulation involves an integrated form of Keller’s equations and leads to a different numerical procedure to solve for the after-impact velocities. In this integral formulation, the kinetic and static friction coefficients are differentiated and any of the three hypotheses of the coefficient of restitution can be employed. Furthermore, a singularity problem that may occur in Keller’s solution is avoided with the integral formulation. Numerical examples are given to illustrate the features of the integral formulation and the differences between the two formulations.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Single-point impact between two rigid bodies

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Figure 2

Configuration of the tangential velocity in the contact plane

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Figure 3

uT versus τ diagram

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Figure 4

θ versus τ diagram

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Figure 5

uT versus τ diagrams: (a) all-the-way sliding; (b) sliding/stopping/sliding; (c) sliding/sticking



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