A spatial revolute joint model with clearance in mechanisms dynamics

CAVALIERI FEDERICO J.; CARDONA ALBERTO

Prague

Congreso; 8th ECCOMAS Thematic Conference on MULTIBODY DYNAMICS 2017; 2017

Czech Republic. Technical University in Prague, Faculty of Mechanical Engineering

Revolute joints are commonly represented with idealized modelsthat restricts the movements of the components of a mechanism by a set of kinematic constraints. In a real mechanism, the inevitablypresence of misalignments, clearance between parts or assemblyerrors strongly affect  the dynamic response of the joints andconsequently of the whole system. These defects generate time variable loads with high frequency which propagates through the system increasing the possibilities of breakages, fatigue or wear damages. Therefore, the mechanical system life is considerably reduced and the operation costs are increased. The penalty approaches are computationally efficient and relatively simple to implement. However, the main drawback associated with this method deals with the difficulty to choose the correct penalties parameters for  the stiffness and damping of the contacting surfaces. Furthermore,  it can introduce high frequency dynamics into the system due to the presence of stiff springs of the contact surfaces. In this work, a new three dimensional revolute joint ispresented, where the clearance and misalignment of thecomponents are taken into account in the formulation. The equationof motion are integrated by using the nonsmooth  alpha generalized scheme asthe proposal of Brüls 2014. Unlike of penalty approaches, the integrator nonsmooth alpha generalized guarantees theexact satisfaction of the bilateral and unilateral constraintsboth at position and velocity levels, avoiding the selection of the penalty parameter and the penetrationbetween the contacting bodies, which is physically unacceptable.The clearance in a joint produces impacts in a small period oftime, thus, the dynamic response of a system is conditioned to acorrect selection of three main variables: i) the time step size;ii) the time integration scheme and iii) the numerical parameters of theintegrators. The standard time integration algorithms as the Newmark family,Hilbert-Hughes-Taylor (HHT) or the generalized alpha, failcompletely in the representation of the impacts process becausethe numeric response generates fictitious energy at contactinstant. In contrast to these integrators, the nonsmooth alpha generalized scheme produces an accurate description of vibration phenomena in non smooth dynamics system with a controllable numerical dissipation. Therefore, the nonsmooth alpha generalized scheme leads to a dynamic response with a qualitatively improved energy behaviour.The proposed joint model is composed by an internal cylinder, named journal and other external cylinder named bearing. Both bodies are considered rigid and without mass properties. Then, if the axial relative displacement between the journal and the bearing are neglected, four different movements which depend on the dynamic system configuration, are allowable: i) free flight: there is no contact between the components; ii) the journal is in contact along a line; iii) the journal is in contact with the bearing at one point; iv)the journal is in contact with the bearing at two opposite points. Therefore, the dynamic behavior of the joint and of the system are related with these four possible configurations, which are depending on the length of the journal and of the clearance. In the no contact condition, the joint does not introduce any forces to the system; on the contrary, in the contact condition, the changes of velocities and accelerations of the joints  modify completely the dynamic of the system.