Revolute joints with clearance in multibody systems P. Flores a , J. Ambr osio b, * a Departamento de Engenharia Mec^ anica, Universidade do Minho, Campus de Azur em, 4800-058 Guimar~ aes, Portugal b Instituto de Engenharia Mec^ anica (IDMEC), Instituto Superior T ecnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal Received 10 March 2004; accepted 12 March 2004 Available online 25 May 2004 Abstract A computational methodology for dynamic analysis of multibody mechanical systems with joint clearance is pre- sented in this work. Clearances always exist in real joints in order to ensure the correct relative motion between the connected bodies being the gap associated to them a result of machining tolerance, wear, and local deformations. Clearance at different joints is the source for impact forces, resulting in wear and tear of the joints, and consequently the degradation of the system performance. The model for planar revolute joints is based on a thorough geometric description of contact conditions and on a continuous contact force model, which represents the impact forces. It is shown that the model proposed here lead to realistic contact forces. These forces correlate well with the joint reaction forces of an ideal revolute joint, which correspond to a null joint clearance. The application to the analysis of a simple planar multibody system illustrates the use of the different models proposed. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Clearance joints; Multibody dynamics; Contact forces; Impact analysis 1. Introduction In general dynamic analysis of multibody mechanical systems it is assumed that the kinematic joints are ideal or perfect, that is, clearance, local deformations, wear, and lubrication effects are neglected. However, in a real mechanical kinematical joint a gap is always present. Such clearance is necessary to allow the relative motion between the connected bodies and to permit the com- ponents assemblage as well. For instance, in a journal– bearing joint there is a radial clearance allowing for the relative motion between the journal and the bearing. This clearance is inevitable due to the machining toler- ances, wear, material deformations, and imperfections. The presence of such joint gaps leads to degradation of the performance of mechanical systems in virtue of the impact forces that take place. Not only these impact forces dissipate energy but they are also a source for vibrations and noise. The general purpose computational tools used for design and analysis of mechanical systems, such as ADAMS [1] or DADS [2], have a wide number of modeling features that require the description of rigid or flexible bodies for which geometry, mass, center of mass, moment of inertia, and other relevant properties are defined. These codes also provide a large library of kinematic joints that constrain relative degrees of free- dom between connected bodies. The kinematic joints available in these commercial programs are represented as ideal joints, i.e., there are no clearances or deforma- tions in them. The subject of the representation of real joints draw the attention of a large number of researchers that produced several theoretical and experimental works devoted to the dynamic simulation of mechanical sys- tems with joint clearances [3–8]. Some of these works focus on the planar systems in which only one kinematic joint is modeled as clearance joint [6,7]. Bengisu et al. [8] presented a study of a four-bar mechanism with multiple * Corresponding author. Tel.: +351-21-8417680; fax: +351- 21-8417915. E-mail address: jorge@dem.ist.utl.pt (J. Ambr osio). 0045-7949/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruc.2004.03.031 Computers and Structures 82 (2004) 1359–1369 www.elsevier.com/locate/compstruc