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Research Papers

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

[+] Author and Article Information
Margarida Machado

CT2M, Mechanical Engineering Department,
University of Minho, Campus Azurém,
Guimarães 4800-058, Portugal
e-mail: margarida@dem.uminho.pt

Paulo Flores

CT2M, Mechanical Engineering Department,
University of Minho, Campus Azurém,
Guimarães 4800-058, Portugal
e-mail: pflores@dem.uminho.pt

Jorge Ambrósio

IDMEC, Instituto Superior Técnico,
University of Lisbon, Av. Rovisco Pais 1,
Lisbon 1049-001, Portugal
e-mail: jorge@dem.ist.utl.pt

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received July 9, 2013; final manuscript received February 16, 2014; published online July 11, 2014. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 9(4), 041010 (Jul 11, 2014) (10 pages) Paper No: CND-13-1175; doi: 10.1115/1.4026894 History: Received July 09, 2013; Revised February 16, 2014

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, and evaluation of the contact forces. The 3D-contact surfaces are generated and represented by using parametric functions due to their simplicity and ease in handling freeform shapes. This task is carried during preprocessing, which is performed before starting the multibody analysis. The preprocessing procedure can be condensed into four steps: a regular and representative collection of surface 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 components of the normal, tangent, and bitangent vectors; the lookup table is rearranged such that the u-v mapping is converted into a 2D matrix being this surface data saved as a direct access file. For the detection of the contact points, the relative distance between the candidate contact points is 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 or pseudopenetration, 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 are used as a demonstrative example. A contact pair is considered between a cup and a marble ball, the contact forces for which are computed using a dissipative contact model.

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Figures

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Fig. 1

Schematic representation of one-eighth of a spherical surface using the parametric method

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Fig. 4

Representation of two generalized contact surfaces

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Fig. 5

Schematic representation of the bilinear interpolation for a surface described by four points

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Fig. 6

Structure of a direct access file of a parametric representation of a surface with 100 points

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Fig. 7

Representation of an update of a storage window

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Fig. 8

Computational algorithm proposed to deal with 3D contact problems in multibody systems

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Fig. 9

Initial configuration of a slider-crank mechanism with a cup (body 5) on the top of the slider and a marble ball (body 6)

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Fig. 10

Illustration of the resultant motion of the MBS in study

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Fig. 11

xy-trajectory of the contact points of the marble ball when using the Hertz law and the Flores et al. model

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Fig. 12

xz-trajectory of the contact points of the marble ball when using the Hertz law and the Flores et al. model

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Fig. 13

Contact indentation between the marble ball and the cup during the first 0.1 s of simulation

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Fig. 14

Force-indentation relations of the contact between the marble ball and the cup during the first 0.1 s of simulation

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Fig. 15

Trajectory of the ball center and the relative contact points during 0.1 s of simulation using two contact force approaches: (a) Hertz law; (b) Flores et al. model

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Fig. 16

Representation of the storage windows

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