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

Abstract

International audienceThis article is devoted to the analysis of the influence of the joint clearances in a mechanism of a circuit breaker, which is a forty-two degrees of freedom mechanism made of seven links, seven revolute joints, and four unilateral contacts with friction. Spatial (3D) revolute joints are modelled 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. Futhermore, 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 to perform the time–integration with 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 methods deals more than seventy 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 to perform a sensitivity analysis using a Monte Carlo method. The numerical results are also validated by careful comparisons with experimental data which show a very good correlation

The contact problem in Lagrangian systems with redundant frictional bilateral and unilateral constraints and singular mass matrix. The all-sticking contacts problem

“…Then the solvability of the contact MLCP holds if and only if ∇h st n,u (q)[z + y] + d dt (∇h st n,u (q) ⊤ )q 0 for some z ∈ R n and y ∈ ker(H st t,u (q) ⊤ ). As alluded to above, this result is also close to [54,Theorem 5], nevertheless the obtained conclusions differ from those in [54, Theorem 5], because we do not introduce Coulomb's friction at the acceleration level as in (5). Indeed this modeling assumption allows one to transform the persistent-sticking mode MLCP in (34) into an LCP, introducing suitable slack variables.…”

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

“…The severity of the contact between the journal and bearing surfaces at a clearance joint was evident by the severity of the local elastic and plastic deformations. Akhadkar et al [420] presented a complete model for three-dimensional revolute joints with dry clearance, which was applied to an industrial circuit breaker system. Moreover, some experimental work was conducted to verify and validate the contact forces developed at joints.…”

Dynamic Response Analysis of Planar Multilink Mechanism considering Wear in Clearances

“…In the actual mechanical mechanism, the clearance of the motion pair is unavoidable [1][2][3][4]. With the development of precision mechanical engineering, it is increasingly necessary to accurately predict the wear phenomenon of mechanical system.…”