INVESTIGADORES
CARDONA alberto
congresos y reuniones científicas
Título:
A spatial revolute joint model with clearance in mechanisms dynamics
Autor/es:
FEDERICO CAVALIERI; ALBERTO CARDONA; OLIVIER BRULS; JAVIER GALVEZ
Lugar:
Praga (Chequia)
Reunión:
Congreso; 8th ECCOMAS Thematic Conference on Multibody Dynamics; 2017
Resumen:
Revolute joints are commonly represented with idealized models that restrict the components movement of the mechanism by a set of kinematic constraints. In a real mechanism, the unavoidable presence of misalignments, clearance between parts and assembly errors strongly affect the joints dynamic response and, consequently, of the whole system. These defects generate time variable loads with high frequency which propagate through the system increasing the possibility of breakage, fatigue and wear damage. Therefore, the mechanical system life is considerably reduced and operation costs are increased. In the last years, several numerical models of joints that include clearance, and where the contact/impact is modeled with a penalty method, have been proposed [1,2, 4]. The penalty approach is relatively simple to implement. However, the main drawback associated with this method is the difficulty to choose the correct penalty parameters for the stiffness and damping of the contacting surfaces. Furthermore, it introduces high frequency dynamics into the system due to the presence of stiff springs that represent the contact surfaces, imposing the use of a very small time step in the integrator to correctly solve the impact. In this work, a new three-dimensional revolute joint is presented, which takes into account the components clearance and misalignment in the formulation. The equations of motion are integrated by using the nonsmoothgeneralized − α scheme proposed by Brüls et al [5]. Unlike the penalty approaches, the nonsmooth generalized − α integrator guarantees the exact satisfaction of bilateral and unilateral constraints both at position and velocity levels, avoiding the need of selecting any penalty parameter. It also avoids any unphysical penetration between the contacting bodies.Joints clearance produces impacts in a small period of time, thus, the dynamic response of a system is conditioned to a correct selection of three main variables: i) the time step size; ii) the time integration scheme and iii) the numerical parameters of the integrators. The standard time integration algorithms such as the Newmark, Hilbert-Hughes-Taylor (HHT) or the smooth generalized − α methods, fail completely in the representation of rigid impacts represented by Lagrange multiplier techniques because the numerical response exhibits an important fictitious energy increase or decrease at the contact instant, completely affecting the computations. In contrast to these integrators, the nonsmooth generalized − α scheme makes an accurate description of impact and vibration phenomena of the system dynamics with a controllable numerical dissipation. Therefore, the nonsmooth generalized − α scheme leads to a a qualitatively improved energy behaviour in the dynamic response.The proposed joint model is composed by an internal cylinder, the journal, and an external cylinder, the bearing (Figure 1). Both bodies are assumed rigid and massless. Then, by ignoring the axial relative displacement between the journal and the bearing, four different movements which depend on the dynamic system configuration, are allowable: i) no contact between the components (free flight); ii) the journal and the bearing are 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 the system is related with these four possible configurations, which depend on the the clearance and on the length of the journal. In the non 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 completely modify the dynamics of the system. To study the behavior of the proposed joint, a spatial three-dimensional mechanism is analyzed (Figure 2). The revolute joint with clearance is situated between the crank and the rigid frame. The dynamic behavior of the system is analyzed by plotting the displacement of the slider. The results are compared with another mechanism composed by ideal joints, i.e. clearance is neglected. Figure 3 shows the time evolution of the position of the slider. The case with clearance iscompared to the ideal case, showing that the dynamic system behavior is affected.