Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T23:58:56.364Z Has data issue: false hasContentIssue false
  • English
  • Français

Multibody modeling of non-planar ball bearings

Published online by Cambridge University Press:  18 December 2013

Christophe Bovet ,
Jean-Marc Linares ,
Laurent Zamponi  and
Emmanuel Mermoz
Christophe Bovet*
Affiliation:
Aix-Marseille Université, CNRS, ISM UMR 7287, 13288 Marseille Cedex 09, France Eurocopter, Aéroport International Marseille Provence, 13725 Marignane, France
Jean-Marc Linares
Affiliation:
Aix-Marseille Université, CNRS, ISM UMR 7287, 13288 Marseille Cedex 09, France
Laurent Zamponi
Affiliation:
Eurocopter, Aéroport International Marseille Provence, 13725 Marignane, France
Emmanuel Mermoz
Affiliation:
Eurocopter, Aéroport International Marseille Provence, 13725 Marignane, France
*
⋆ Corresponding author:christophe.bovet@etu.univ-amu.fr

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This work presents the dynamic modeling of ball bearing which uses multibody dynamicformalism. Such formalism allows immediate integration of the model in dynamic simulationsof helicopter main gear boxes. Ball bearing is considered non-lubricated in order topredict its behavior in case of lubrication system failure. Rolling contacts are treatedwith the method proposed by Kalker. This approach is based on polynomial approximation ofrelative displacement on the contact ellipse. For low computational cost and without anyspatial discretization, it gives a good estimation of tangential traction and creep. Also,a regularization of the Kalker linear creep theory is proposed. It is used here tofacilitate the global convergence of the Newton iterative process. It is well suited formultibody dynamic simulations which do not need a very fine treatment of rolling contact.A numerical example of a ball bearing under thrust load is presented.

Keywords

Multibody dynamicBall bearingRolling contactKalker creep theoryDynamique multicorpsRoulement à billeContact roulantTheorie de Kalker
Type
Research Article
Information
Mechanics & Industry , Volume 14 , Issue 5 , 2013 , pp. 335 - 345
Copyright
© AFM, EDP Sciences 2013

References

T.A. Harris, M.N. Kotzalas, Rolling bearing analysis, Wiley New York, 2001
P.K. Gupta, Advanced dynamics of rolling elements, Springer-Verlag, 1984
Tiwari, M., Gupta, K., Prakash, O., Effect of radial internal clearance of a ball bearing on the dynamics of a balanced horizontal rotor, J. Sound Vib. 238 (2000) 723–756 CrossRefGoogle Scholar
Harsha, S.P., Nonlinear dynamic response of a balanced rotor supported by rolling element bearings due to radial internal clearance effect, Mech. Mach. Theory 41 (2006) 688–706 CrossRefGoogle Scholar
Tandon, N., Choudhury, A., An analytical model for the prediction of the vibration response of rolling element bearings due to a localized defect, J. Sound Vib. 205 (1997) 275–292 CrossRefGoogle Scholar
Changqing, B., Qingyu, X., Dynamic model of ball bearings with internal clearance and waviness, J. Sound Vib. 294 (2009) 23–48 CrossRefGoogle Scholar
Bourdon, A., Bordegaray, C., Études comparatives de plusieurs modèles de la rigidité des roulements sur le comportement dynamique d’une boîte de vitesses automobile, Mécanique & Industries 8 (2007) 35–49 CrossRefGoogle Scholar
Zamponi, L., Mermoz, E., Linares, J.M., Étude des méthodes de calcul des pressions de contact dans les roulements à pistes intégrées des boîtes de transmission aéronautiques, Mécanique & Industries 8 (2007) 567–575 CrossRefGoogle Scholar
A.A. Shabana, Dynamics of Multibody Systems, Cambridge University Press, 2005
M. Géradin, A. Cardona, Flexible multibody dynamics: a finite element approach, John Wiley, 2001
Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M., Koshy, C.S., Lubricated revolute joints in rigid multibody systems, Nonlinear Dynamic 56 (2009) 277–295 CrossRefGoogle Scholar
Tian, Q., Zhang, Y., Chen, L., Flores, P., Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints, Comput. Struct. 87 (2009) 913–929 CrossRefGoogle Scholar
Xu, L., Yang, Y., Li, Y., Li, C., Wang, S., Modeling and analysis of planar multibody systems containing deep groove ball bearing with clearance, Mech. Mach. Theory 56 (2012) 69–88 CrossRefGoogle Scholar
Stacke, L.E., Fritzson, D., Nordling, P., BEAST-a rolling bearing simulation tool, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 213 (1999) 63–71 Google Scholar
J.J. Kalker, On the Rolling Contact of Two Elastic Bodies in the Presence of Dry Friction, Thesis, Delft University of Technology, 1967
Chevalier, L., Cloupet, S., Eddhahak-Ouni, A., Contributions à la modélisation simplifiée de la mécanique des contacts roulants, Mécanique & Industries 7 (2005) 155–168 CrossRefGoogle Scholar
Géradin, M., Cardona, A., Kinematics and dynamics of rigid and flexible mechanisms using finite elements and quaternion algebra, Comput. Mech. 4 (1988) 115–135 CrossRefGoogle Scholar
Hilber, H.M., Hughes, T., Taylor, R.L., Improved numerical dissipation for time integration algorithms in structural dynamics, Earthquake Eng. Struct. Dyn. 5 (1977) 283–292 CrossRefGoogle Scholar
K.L. Johnson, Contact Mechanics, Cambridge University Press, 1987
Oden, J.T., Martins, J.A.C., Models and computational methods for dynamic friction phenomena, Comput. Methods Appl. Mech. Eng. 52 (1985) 527–634 CrossRefGoogle Scholar
Machado, M., Moreira, P., Flores, P., Lankarani, H.M., Compliant contact force models in multibody dynamics: Evolution of the Hertz contact theory, Mech. Mach. Theory 53 (2012) 99–121 CrossRefGoogle Scholar