A Lookup Table-Based Approach for Spatial Analysis of Contact Problems

Abstract

The aim of this work is to present an efficient methodology to deal with general 3D-contact problems. This approach embraces three steps: geometrical definition of 3D-surfaces; detection of the candidate contact points; evaluation of the contact forces. The 3D-contact surfaces are generated and represented by using parametric functions due to their simplicity and easiness to handle freeform shapes. This task is carried in preprocessing, performed preliminarily to the implementation of the multibody code. The preprocessing procedure can be condensed into four steps: a regular and representative surface collection of points is extracted from the 3D-parametric surface; for each point the tangent vectors to the u and v directions of the parametric surface and the normal vector are computed; the geometrical information on each point is saved in a lookup table, including the parametric point coordinates, the corresponding Cartesian coordinates and the Cartesian components of the normal, tangent and binormal vectors; the lookup table is rearranged such that the u-v mapping is converted into a 3D-matrix form. In the last step, the surface data is saved as a direct access file. Regarding the detection of the contact points, the relative distance between the candidate contact points are computed and used to check if the bodies are in contact. The actual contact points are selected as those that correspond to the maximum relative indentation. The contact forces are determined as functions of the indentation, impact velocity and geometric and material properties of the contacting surfaces. In general, lookup tables are used to reduce the computation time in dynamic simulations. However, the application of these schemes involves an increase of memory needs. Within the proposed approach, the amount of memory used is significantly reduced, as a result of a partial upload into memory of the lookup table. A slider-crank mechanism with a cup on the top of the slider and a marble ball is used as demonstrative example. A contact pair is considered between a cup and a marble ball, being the contact forces computed using a dissipative contact model.