Lubricated revolute joints in rigid multibody systems

The main purpose of this work is to present a general methodology for modeling lubricated revolute joints in constrained rigid multibody systems. In the dynamic analysis of journal-bearings, the hydrodynamic forces, which include both squeeze and wedge effects, generated by the lubricant fluid, oppose the journal motion. The hydrodynamic forces are obtained by integrating the pressure distribution evaluated with the aid of Reynolds’ equation, written for the dynamic regime. The hydrodynamic forces built up by the lubricant fluid are evaluated from the system state variables and included into the equations of motion of the multibody system. Numerical examples are presented in order to demonstrate the use of the methodologies and procedures described in this work.Fundação para a Ciência e a Tecnologia (FCT

Strain-Based Analysis for Geometrically Nonlinear Beams: A Modal Approach

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97066/1/AIAA2012-1713.pd

A comparison of Finite Elements for Nonlinear Beams: The absolute nodal coordinate and geometrically exact formulations

Two of the most popular finite element formulations for solving nonlinear beams are the absolute nodal coordinate and the geometrically exact approaches. Both can be applied to problems with very large deformations and strains, but they differ substantially at the continuous and the discrete levels. In addition, implementation and run-time computational costs also vary significantly. In the current work, we summarize the main features of the two formulations, highlighting their differences and similarities, and perform numerical benchmarks to assess their accuracy and robustness. The article concludes with recommendations for the choice of one formulation over the other

Spatial rigid-multi-body systems with lubricated spherical clearance joints : modeling and simulation

The dynamic modeling and simulation of spatial rigid-multi-body systems with lubricated spherical joints is the main purpose of the present work. This issue is of paramount importance in the analysis and design of realistic multibody mechanical systems undergoing spatial motion. When the spherical clearance joint is modeled as dry contact; i.e., when there is no lubricant between the mechanical elements which constitute the joint, a body-to-body (typically metal-to-metal) contact takes place. The joint reaction forces in this case are evaluated through a Hertzian-based contact law. A hysteretic damping factor is included in the dry contact force model to account for the energy dissipation during the contact process. The presence of a fluid lubricant avoids the direct metal-to-metal contact. In this situation, the squeeze film action, due to the relative approaching motion between the mechanical joint elements, is considered utilizing the lubrication theory associated with the spherical bearings. In both cases, the intra-joint reaction forces are evaluated as functions of the geometrical, kinematical and physical characteristics of the spherical joint. These forces are then incorporated into a standard formulation of the system’s governing equations of motion as generalized external forces. A spatial four bar mechanism that includes a spherical clearance joint is considered here as example. The computational simulations are carried out with and without the fluid lubricant, and the results are compared with those obtained when the system is modeled with perfect joints only. From the general results it is observed that the system’s performance with lubricant effect presents fewer peaks in the kinematic and dynamic outputs, when compared with those from the dry contact joint model.Fundação para a Ciência e a Tecnologia (FCT

A parametric study on the dynamic response of planar multibody systems with multiple clearance joints

A general methodology for dynamic modeling and analysis of multibody systems with multiple clearance joints is presented and discussed in this paper. The joint components that constitute a real joint are modeled as colliding bodies, being their behavior influenced by geometric and physical properties of the contacting surfaces. A continuous contact force model, based on the elastic Hertz theory together with a dissipative term, is used to evaluate the intra-joint contact forces. Furthermore, the incorporation of the friction phenomenon, based on the classical Coulomb’s friction law, is also discussed. The suitable contact-impact force models are embedded into the dynamics of multibody systems methodologies. An elementary mechanical system is used to demonstrate the accuracy and efficiency of the presented approach, and to discuss the main assumptions and procedures adopted. Different test scenarios are considered with the purpose of performing a parametric study for quantifying the influence of the clearance size, input crank speed and number of clearance joints on the dynamic response of multibody systems with multiple clearance joints. Additionally, the total computation time consumed in each simulation is evaluated in order to test the computational accuracy and efficiency of the presented approach. From the main results obtained in this study, it can be drawn that clearance size and the operating conditions play a crucial role in predicting accurately the dynamic responses of multibody systems.Fundação para a Ciência e a Tecnologia (FCT

On the constraints violation in forward dynamics of multibody systems

It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton-Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian and the coordinate partitioning method.The first author expresses his gratitude to the Portuguese Foundation for Science and Technology through the PhD grant (PD/BD/114154/2016). This work has been supported by the Portuguese Foundation for Science and Technology with the reference project UID/EEA/04436/2013, by FEDER funds through the COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) with the reference project POCI-01-0145-FEDER-006941.info:eu-repo/semantics/publishedVersio

A Self-Stabilized Algorithm for Enforcing Constraints in Multibody Systems

A new algorithm is developed for the enforcement of constraints within the framework of nonlinear, flexible multi-body system modeled with the finite element approach. The proposed algorithm exactly satisfies the constraints at the displacement and velocity levels, and furthermore, it achieves nonlinear unconditional stability by imposing the vanishing of the work done by the constraint forces when combined with specific discretizations of the inertial and elastic forces. Identical convergence rates are observed for the displacements, velocities, and Lagrange multipliers. The proposed algorithm is closely related to the stabilized index-2 or GGL method, although no additional multipliers are introduced in the present approach. These desirable characteristics are obtained without resorting to numerically dissipative algorithms. If high frequencies are present in the system, i.e. the system is physically stiff, dissipative schemes become necessary; the proposed algorithm is extended to deal with this situation. (C) 2003 Elsevier Science Ltd. All rights reserved