Study of the effect of contact force model on the dynamic response of mechanical systems with dry clearance joints : computational and experimental approaches

The main objective of this work is to present a computational and experimental study on the contact forces developed in revolute clearance joints. For this purpose, a well-known slider-crank mechanism with a revolute clearance joint between the connecting rod and slider is utilized. The intra-joint contact forces that generated at this clearance joints are computed by considered several different elastic and dissipative approaches, namely those based on the Hertz contact theory and the ESDU tribology-based for cylindrical contacts, along with a hysteresis-type dissipative damping. The normal contact force is augmented with the dry Coulomb’s friction force. In addition, an experimental apparatus is use to obtained some experimental data in order to verify and validate the computational models. From the outcomes reported in this paper, it is concluded that the selection of the appropriate contact force model with proper dissipative damping plays a significant role in the dynamic response of mechanical systems involving contact events at low or moderate impact velocities.Fundação para a Ciência e a Tecnologia (FCT

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

On the contact detection for contact-impact analysis in multibody systems

One of the most important and complex parts of the simulation of multibody systems with contact-impact involves the detection of the precise instant of impact. In general, the periods of contact are very small and, therefore, the selection of the time step for the integration of the time derivatives of the state variables plays a crucial role in the dynamics of multibody systems. The conservative approach is to use very small time steps throughout the analysis. However, this solution is not efficient from the computational view point. When variable time step integration algorithms are used and the pre-impact dynamics does not involve high-frequencies the integration algorithms may use larger time steps and the contact between two surfaces may start with initial penetrations that are artificially high. This fact leads either to a stall of the integration algorithm or to contact forces that are physically impossible which, in turn, lead to post-impact dynamics that is unrelated to the physical problem. The main purpose of this work is to present a general and comprehensive approach to automatically adjust the time step, in variable time step integration algorithms, in the vicinity of contact of multibody systems. The proposed methodology ensures that for any impact in a multibody system the time step of the integration is such that any initial penetration is below any prescribed threshold. In the case of the start of contact, and after a time step is complete, the numerical error control of the selected integration algorithm is forced to handle the physical criteria to accept/reject time steps in equal terms with the numerical error control that it normally uses. The main features of this approach are the simplicity of its computational implementation, its good computational efficiency and its ability to deal with the transitions between non contact and contact situations in multibody dynamics. A demonstration case provides the results that support the discussion and show the validity of the proposed methodology.Fundação para a Ciência e a Tecnologia (FCT

Coupling dynamics of a geared multibody system supported by Elastohydrodynamic lubricated cylindrical joints

A comprehensive computational methodology to study the coupling dynamics of a geared multibody system supported by ElastoHydroDynamic (EHD) lubricated cylindrical joints is proposed throughout this work. The geared multibody system is described by using the Absolute-Coordinate-Based (ACB) method that combines the Natural Coordinate Formulation (NCF) describing rigid bodies and the Absolute Nodal Coordinate Formulation (ANCF) characterizing the flexible bodies. Based on the finite-short bearing approach, the EHD lubrication condition for the cylindrical joints supporting the geared system is considered here. The lubrication forces developed at the cylindrical joints are obtained by solving the Reynolds’ equation via the finite difference method. For the evaluation of the normal contact forces of gear pair along the Line Of Action (LOA), the time-varying mesh stiffness, mesh damping and Static Transmission Error (STE) are utilized. The time-varying mesh stiffness is calculated by using the Chaari’s methodology. The forces of sliding friction along the Off-Line-Of-Action (OLOA) are computed by using the Coulomb friction models with a time-varying coefficient of friction under the EHD lubrication condition of gear teeth. Finally, two numerical examples of application are presented to demonstrate and validate the proposed methodology.National Natural Science Foundations of China under Grant 11290151, 11221202 and 11002022, Beijing Higher Education Young Elite Teacher Project under Grant YETP1201

Modeling and simulation of joint clearance effects on mechanisms having rigid and flexible links

In this study, kinematic and dynamic characteristics of a planar four-bar mechanism having joint clearance and link flexibility are investigated. Assuming that joint clearance as a virtual massless link, artificial clearances are developed at crank-coupler and coupler-follower joints. Contact model in joints with clearance is established using the nonlinear spring-damper model and the friction effect is considered using the Coulomb friction model. Then the simulation is implemented and the kinematic and dynamic characteristics of model mechanism are investigated. The computational methodology can predict the effects of clearance on planar mechanism having rigid and flexible links. The results are evaluated for the case of stationary phase, and naturally show that extreme values occur in output of the mechanism with clearances. Due primarily to the suspension effect of the flexible link, values of these peaks in the flexible mechanism decrease relative to that of the rigid mechanism. In addition, the flexibility has a significant effect on the vibration response of the mechanism with joint clearance

Prediction of vibration characteristics of a planar mechanism having imperfect joints using neural network

Clearance is inevitable in the joints of mechanisms due primarily to the design, manufacturing and assembly processes or a wear effect. Excessive value of joint clearance plays a crucial role and has a significant effect on the kinematic and dynamic performances of the mechanism. In this study, effects of joint clearances on bearing vibrations of mechanism are investigated. An experimental test rig is set up, and a planar slider-crank mechanism having two imperfect joints with radial clearance is used as a model mechanism. Three accelerometers are positioned at different points to measure the bearing vibrations during the mechanism motion. For the different running speeds and clearance sizes, this work provides a neural model to predict and estimate the bearing vibrations of the mechanical systems having imperfect joints. The results show that radial basis function (RBF) neural network has a superior performance for predicting and estimating the vibration characteristics of the mechanical system