Research Papers

Volumetric Modeling and Experimental Validation of Normal Contact Dynamic Forces

[+] Author and Article Information
Michael Boos

Ph.D. Student
e-mail: mboos@uwaterloo.ca

John McPhee

Fellow ASME
Department of Systems Design Engineering,
University of Waterloo,
Waterloo, ON, N2L 3G1, Canada
e-mail: mcphee@uwaterloo.ca

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 19, 2011; final manuscript received April 23, 2012; published online July 23, 2012. Assoc. Editor: Dan Negrut.

J. Comput. Nonlinear Dynam 8(2), 021006 (Jul 23, 2012) (8 pages) Paper No: CND-11-1155; doi: 10.1115/1.4006836 History: Received September 19, 2011; Revised April 23, 2012

A volumetric contact dynamics model has been proposed for the purpose of generating reliable and rapid simulations of contact dynamics. Forces and moments between bodies in contact can be expressed in terms of the volume of interference between the undeformed geometries. This allows for the modeling of contact between complex geometries and relatively large contact surfaces, while being computationally less expensive than finite element methods. However, the volumetric model requires experimental validation. Models for simple geometries in contact have been developed for stationary and dynamic contact, and an apparatus has been developed to experimentally validate these models. This paper focuses on validation of the normal contact models. Measurements of forces and displacements will be used to identify the parameters related to the normal force, i.e., the volumetric stiffness and hysteretic damping factor for metallic surfaces. The experimental measurements are compared with simulated results to assess the validity of the volumetric model.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


de Carufel, J., Martin, E., and Piedbœuf, J.-C., 2000, “Control Strategies for Hardware-In-The-Loop Simulation of Flexible Space Robots,” IEEE Proc.: Control Theory Appl., 147(6), pp. 569–579. [CrossRef]
Gonthier, Y., McPhee, J., Lange, C., and Piedbœuf, J.-C., 2004, “A Regularized Contact Model With Asymmetric Damping and Dwell-Time Dependent Friction,” Multibody Syst. Dyn., 11(3), pp. 209–233. [CrossRef]
Gilardi, G., and Sharf, I., 2002, “Literature Survey of Contact Dynamics Modelling,” Mech. Mach. Theory, 37, pp. 1213–1239. [CrossRef]
Hertz, H., 1896, Miscellaneous Papers by H. Hertz, D. E.Jones and G.Schott, eds., Macmillan, London.
Hunt, K., and Crossley, F., 1975, “Coefficient of Restitution Interpreted as Damping in Vibroimpact,” J. Appl. Mech., 7, pp. 440–445. [CrossRef]
Janabi-Sharifi, F., 1995, “Collision: Modeling, Simulation and Identification Of Robotic Manipulators Interacting With Environments,” J. Intell. Robotic Syst., 13(1), pp. 1–44. [CrossRef]
Lankarani, H. M., and Nikravesh, P. E., 1994, “Continuous Contact Force Models for Impact Analysis in Multibody Systems,” Nonlinear Dyn., 5, pp. 193–207.
Johnson, K., 1985, Contact Mechanics, Cambridge University Press, London.
Goldsmith, W., 1960, Impact: The Theory and Physical Behavior of Colliding Solids, Edward Arnold Ltd., London.
Marhefka, D., and Orin, D., 1999, “A Compliant Contact Model With Nonlinear Damping for Simulation of Robotic Systems,” IEEE Trans. Syst., Man Cybern., Part A. Syst. Humans, 29(6), pp. 566–572. [CrossRef]
Flores, P., Machado, M., Silva, M., and Martins, J., 2011, “On the Continuous Contact Force Models for Soft Materials in Multibody Dynamics,” Multibody Syst. Dyn., 25, pp. 357–375. [CrossRef]
Diolaiti, N., Melchiorri, C., and Stramigioli, S., 2005, “Contact Impedance Estimation for Robotic Systems,” IEEE Trans. Rob., 21(5), pp. 925–935. [CrossRef]
Stoianovici, D., and Hurmuzlu, Y., 1996, “A Critical Study of the Applicability of Rigid-Body Collision Theory,” ASME J. Applied Mech., 63, pp. 307–316. [CrossRef]
Vu-Quoc, L., and Zhang, X., 1999, “An Elasto-Plastic Contact Force-Displacement Model in the Normal Direction: Displacement-Driven Version,” Proc. R. Soc. London, Ser. A, 455(1991), pp. 4013–4044. [CrossRef]
Vu-Quoc, L., Zhang, X., and Lesburg, L., 2000, “A Normal Force-Displacement Model for Contacting Spheres, Accounting for Plastic Deformation: Force-Driven Formulation,” J. Appl. Mech., 67(2), pp. 363–371. [CrossRef]
Zhang, X., and Vu-Quoc, L., 2002, “A Method to Extract the Mechanical Properties of Particles in Collision Based on a new Elastoplastic Normal Force-Displacement Model,” Mech. Mater., 34(12), pp. 779–794. [CrossRef]
Plantard, G., and Papini, M., 2005, “Mechanical and Electrical Behaviors of Polymer Particles. Experimental Study of the Contact Area Between two Particles. Experimental Validation of a Numerical Model,” Granular Matter, 7(1), pp. 1–12. [CrossRef]
Gonthier, Y., McPhee, J., Lange, C., and Piedbœuf, J.-C., 2005, “A Contact Modeling Method Based on Volumetric Properties,” Proceedings of the 2005 ASME Design Engineering Technical Conferences and 5th International Conference on Multibody Systems, Nonlinear Dynamics and Control, Vol. 2005, pp. 477–486.
Gonthier, Y., 2007, “Contact Dynamics Modelling for Robotic Task Simulation,” Ph.D. thesis, University of Waterloo, West Waterloo, ON, Canada.
Roy, A. R., and Carretero, J. A., 2009, “A volume-Based Contact Dynamics Model With Asymmetric Damping Independent of the Coefficient of Restitution,” Proceedings of the 2009 CCToMM Mechanisms, Machines, and Mechatronics Symposium.
Harris, J. W., and Stocker, H., 1998, Handbook of Mathematics and Computational Science, Springer-Verlag, New York.
Sneddon, I. N., 1965, “The Relation Between Load and Penetration in the Axisymmetric Boussinesq Problem for a Punch of Arbitrary Profile,” Int. J. Eng. Sci., 3(1), pp. 47–57. [CrossRef]
Munisamy, R. L., Hills, D. A., and Nowell, D., 1995, “The Solution of the Contact Between a Tilted Circular Rigid Punch and an Elastic Half-Space,” Wear, 184(1), pp. 93–95. [CrossRef]
Verscheure, D., Sharf, I., Bruyninckx, H., Swevers, J., and Schutter, J. D., 2009, “Identification of Contact Dynamics Parameters for Stiff Robotic Payloads,” IEEE Trans. Rob., 25(2), pp. 240–252. [CrossRef]


Grahic Jump Location
Fig. 1

Volume of interference between two bodies in contact

Grahic Jump Location
Fig. 3

Normal force configuration of the apparatus

Grahic Jump Location
Fig. 2

Mechanical apparatus for contact experiments, shown in the normal configuration

Grahic Jump Location
Fig. 4

Quasi-static force versus displacement for spherical contact on aluminum

Grahic Jump Location
Fig. 5

Quasi-static force versus displacement for spherical contact on magnesium alloy

Grahic Jump Location
Fig. 8

Force and displacement measurements for impact at 0.58 mm/s on magnesium alloy

Grahic Jump Location
Fig. 9

Estimated hysteretic damping factors plotted by impact velocity

Grahic Jump Location
Fig. 6

Quasi-static force versus displacement for cylindrical contact on aluminum

Grahic Jump Location
Fig. 7

Quasi-static force versus displacement for cylindrical contact on magnesium alloy



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In