Multibody System Dynamics

, Volume 42, Issue 3, pp 249–282 | Cite as

Multibody systems with 3D revolute joints with clearances: an industrial case study with an experimental validation

  • Narendra Akhadkar
  • Vincent Acary
  • Bernard Brogliato


This article is devoted to the analysis of the influence of the joint clearances in a mechanism of a circuit breaker, which is a 42 degree-of-freedom mechanism made of seven links, seven revolute joints, and four unilateral contacts with friction. Spatial (3D) revolute joints are modeled with both radial and axial clearances taking into account contact with flanges. Unilateral contact, Coulomb’s friction and Newton impact laws are modeled within the framework of nonsmooth mechanics without resorting to some regularizations or compliance/damping at contact. The nonsmooth contact dynamics method based on an event-capturing time-stepping scheme with a second order cone complementarity solver is used to perform the numerical integration. Furthermore, the stabilization of the constraints at the position level is made thanks to the stabilized combined projected Moreau–Jean scheme. The nonsmooth modeling approach together with an event–capturing time-stepping scheme allows us to simulate, in an efficient and robust way, the contact and impacts phenomena that occur in joints with clearances. In particular, comparing with the event-detecting time-stepping schemes, the event-capturing scheme enables us to perform the time-integration with a large number of events (impacts, sliding/sticking transitions, changes in the direction of sliding) and possibly with finite-time accumulations with a reasonable time-step length. Comparing with compliant contact models, we avoid stiff problems related with high stiffnesses at contact which generate some issues in contact stabilization and spurious oscillations during persistent contact periods. In the studied mechanisms of the circuit breakers, the numerical method deals with more than 70 contact points without any problems. Furthermore, the number of contact parameters is small—one coefficient of restitution and one coefficient of friction. Though they are sometimes difficult to measure accurately, the sensitivity of the simulation result with respect to contact parameters is low in the mechanism of the circuit breaker. It is demonstrated that this method, thanks to its robustness and efficiency, allows us to perform a sensitivity analysis using a Monte Carlo method. The numerical results are also validated by careful comparisons with experimental data, showing a very good correlation.


Joint clearance Unilateral constraints Coulomb’s friction Impacts Stabilized combined Moreau–Jean time-stepping scheme Sensitivity analysis Experimental validation Circuit breaker 


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Narendra Akhadkar
    • 1
  • Vincent Acary
    • 2
  • Bernard Brogliato
    • 2
  1. 1.Schneider ElectricGrenobleFrance
  2. 2.INRIA Grenoble Rhône-Alpes, Laboratoire Jean KuntzmanUniversity Grenoble-AlpesSaint IsmierFrance

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