José Carlos Pimenta Claro

Influence of the contact–impact force model on the dynamic response of multi-body systems

Abstract This work deals with contact—impact force models for both spherical and cylindrical contact surfaces. The incorporation of the friction phenomenon, based on the Coulomb friction law, is also discussed together with an effective computational strategy, which includes the automatic step size selection procedure. Impacts within a revolute clearance joint in a basic slider—crank mechanism are used as an example to compare the different contact force models. The collision is a prominent phenomenon in many multi-body systems such as mechanisms with intermittent motion, kinematic discontinuities, and clearance joints. As a result of an impact, the values of the system state variables change very fast, eventually looking like discontinuities in the system velocities and accelerations. The impact is characterized by large forces that are applied and removed in a short time period. The knowledge of the peak forces developed in the impact process is very important for the dynamic analysis of multi-body systems and it has consequences in the design process. The model for the contact—impact force must consider the material and geometric properties of the colliding surfaces, consider information on the impact velocity, contribute to an efficient integration, and account for some level of energy dissipation. These characteristics are ensured with a continuous contact force model, in which the deformation and contact forces are considered as continuous functions.

Dynamic behaviour of planar rigid multi-body systems including revolute joints with clearance

Abstract This paper deals with a general methodology to assess the influence of the clearance size and the friction coefficient on the dynamic response of planar rigid multi-body systems including revolute joints with clearance. When there is a clearance in a revolute joint, impacts between the journal and the bearing can occur, and consequently, local deformations take place. The impact is internal and the response of the system is performed using a continuous contact force model. The friction effect because of the contact between joint elements is also included. The dynamic response of the systems is obtained numerically by solving the constraint equations and the contact-impact forces produced in the clearance joint, simultaneously with the differential equations of motion and a set of initial conditions. Numerical results for two simple mechanisms with revolute clearance joints are presented and discussed. In the present work, the clearance size and friction effects are analysed separately. Through the use of Poincaré maps, both periodic and chaotic responses of the systems are observed. The results predict the existence of the periodic or regular motion at certain clearance sizes and friction coefficients and chaotic or non-linear in other cases.

Dynamics of Multibody Systems With Spherical Clearance Joints

This work deals with a methodology to assess the influence of the spherical clearance joints in spatial multibody systems. The methodology is based on the Cartesian coordinates, being the dynamics of the joint elements modeled as impacting bodies and controlled by contact forces. The impacts and contacts are described by a continuous contact force model that accounts for geometric and mechanical characteristics of the contacting surfaces. The contact force is evaluated as function of the elastic pseudo-penetration between the impacting bodies, coupled with a nonlinear viscous-elastic factor representing the energy dissipation during the impact process. A spatial four bar mechanism is used as an illustrative example and some numerical results are presented, being the efficiency of the developed methodology discussed in the process of their presentation. The results obtained show that the inclusion of clearance joints in the modelization of spatial multibody systems significantly influences the prediction of components’ position and drastically increases the peaks in acceleration and reaction moments at the joints. Moreover, the system’s response clearly tends to be nonperiodic when a clearance joint is included in the simulation.Copyright

Translational Joints With Clearance in Rigid Multibody Systems

A computational methodology for dynamic description of rigid multibody systems with translational clearance joints is presented and discussed in this work. Over the past years, extensive work has been done to study the dynamic effect of the revolute joints with clearance in multibody systems, in contrast with the little work devoted to model translational joints with clearance. In a joint with translation clearance, there are many possible ways to set the physical configuration between the slider and guide, namely: (i) no contact between the two elements, (ii) one corner of the slider in contact with the guide surface, (iii) two adjacent slider corners in contact with the guide surface, and (iv) two opposite slider corners in contact with the guide surfaces. The proposed methodology takes into account these four different situations. The conditions for switching from one case to another depend on the system dynamics configuration. The existence of a clearance in a translational joint removes two kinematic constraints from a planar system and introduces two extra degrees of freedom in the system. Thus, a translational clearance joint does not constrain any degree of freedom of the mechanical system but it imposes some restrictions on the slider motion inside the guide limits. When the slider reaches the guide surfaces, an impact occurs and the dynamic response of the joint is modeled by contact-impact forces. These forces are evaluated here with continuous contact force law together with a dissipative friction force model. The contact-impact forces are introduced into the systems equations of motion as external generalized forces. The proposed methodology is applied to a planar multibody mechanical system with a translational clearance joint in order to demonstrate its features.

An Experimental Investigation of the Effect of Groove Location and Supply Pressure on the THD Performance of a Steadily Loaded Journal Bearing

This paper aims to present the results of parametric experiments carried out in order to study the influence of groove location and supply pressure on the performance of a steadily loaded journal bearing with a single-axial groove, Hydrodynamic pressure and temperature distributions on the bush surface, shaft temperature, flow rate and bush torque were measured at variable supply pressure, using bushes with a single groove located at three different positions. A series of tests were carried out for variable applied load and rotational speed. The experimental evidence shows that some bearing characteristics are significantly sensitive to changes in groove location and supply pressure. One groove located at 30 degrees in relation to the load line, in the direction of shaft rotation, can conduct to reductions in maximum temperature, maximum hydrodynamic pressure and bush torque, with a moderate increase in oil flow rate.

An analysis of the influence of oil supply conditions on the thermohydrodynamic performance of a single groove journal bearing

Abstract In this work a thermohydrodynamic analysis has been developed in order to investigate the influence of oil supply conditions on the performance of a journal bearing. The supply conditions considered were oil supply temperature, supply pressure, groove length and groove location. To carry out this study, the hydrodynamic pressure distribution inside the bearing has been determined using a mass-conserving cavitation model with realistic supply conditions. The energy equation and the heat conduction equation have been used for the determination of oil film and bush temperature distributions. The agreement observed between theoretical predictions and experimental published data is acceptable. Quantitative information shows that the oil supply conditions affect bearing performance parameters in different ways. Oil flowrate was markedly affected by all supply parameters studied. Power loss, maximum bush temperature and minimum film thickness were mainly dependent on oil supply temperature. The effect of supply pressure on minimum film thickness was dependent on groove location. An axial groove located at 90° to the load line gave rise to more favourable bearing performance characteristics.

An experimental study of the influence of loading direction on the thermohydrodynamic behaviour of twin axial groove journal bearing

An experimental assessment of the influence of angle between the groove axis and the load line on the thermohydrodynamic behaviour of twin groove hydrodynamic journal bearings has been undertaken. At nine different loading direction angles, the oil–bush interface temperature profiles, oil outlet temperature, maximum bush temperature, total flow rate, and oil flow rate through each groove were measured for variable applied load and oil supply pressure while the feeding temperature was kept constant (40°C). To the authors’ knowledge, this is the first study of the influence of loading direction on the performance of journal bearing with two axial grooves in which the flow rate were measured in each groove for different working conditions under laminar regime. It was found that the variation of loading direction has a strong effect on the bearing performance. Under some running conditions, negative lubricant flow rate (hot oil reflux) at one groove was detected. This seldom-reported phenomenon was found to affect the bearing performance dramatically. Increasing supply pressure yielded a temperature decrease, especially for high loads, and sometimes prevented the occurrence of hot oil reflux.

Analysis of Hydrodynamic Journal Bearings Considering Lubricant Supply Conditions

A method of analysis of steadily loaded hydrodynamic journal bearings with a single axial groove (either on the load line or at 90° to the load line) or two diametrically opposed axial grooves is described. The method is based on Elrods cavitation algorithm (which ensures conservation of mass flow in both the full film and the cavitated regions) and is able to accommodate specified lubricant supply conditions, namely groove size and location and supply pressure. Special attention has been given to the determination of flowrate. The equation governing the distribution of pressure around the bearing has been solved numerically using a finite differences approximation and multi-grid techniques to accelerate the convergence of the solution. Performance predictions of the analysis are compared with published experimental data and with experimental measurements obtained in laboratory tests carried out by the authors. The data used cover all grooving arrangements studied.

Thermohydrodynamic modelling of journal bearings under varying load angle and negative groove flow rate

The performance of hydrodynamic journal bearings is affected by the conditions under which the lubricant is fed to the bearing gap. Axial grooves are often used and, depending on their location relatively to the load line, they might substantially interfere with the hydrodynamic pressure generation and the thermal behaviour of the bearing. However, many of the existing tools for predicting bearing performance are not able to suitably predict bearing behaviour under varying load angle given the oversimplified way under which they treat lubricant feeding conditions. The present work proposes a detailed thermohydrodynamic approach which realistically incorporates these conditions into the bearing analysis. Special care is put on the mass and energy-conserving models of the ruptured film region and on a detailed treatment of lubricant mixing within the vicinity of grooves. This includes the first full modelling of the effect of negative flow rate in a groove, a phenomenon originally described experimentally in detail by the authors in previous publications, and which happens for a broad range of load/groove angles. An extensive investigation on the influence of loading direction on the performance of twin groove journal bearings has been performed. This parameter is found to affect deeply all major performance parameters due to the interference of groove regions in the hydrodynamic pressure generation and in the flow rates at each groove.

An experimental investigation on the influence of deactivation of a groove on the performance of a twin groove journal bearing

Laboratory tests have been carried out in order to assess the influence of groove activation and deactivation on the performance of a twin axial groove steadily loaded hydrodynamic journal bearing. Temperature distribution at the oil–bush interface, oil outlet temperature, total oil flow rate, partial oil flow rate (at each groove), and motor consumption were measured for several journal speeds and loads under constant feeding pressure (pf) and constant feeding temperature (Tf), at five different loading angles (Γ). In this study, the corresponding groove was deactivated whenever negative oil flow rate was observed in it and results were compared. It was found that the groove deactivation strategy has profound influence on the bearing performance when negative flow rate occurs at one groove, preventing such undesirable effects as lubricant starvation at the loaded region of the bearing. Groove deactivation in the event of negative flow rate may be easily implemented by incorporating a check valve to the feeding system of each groove. Such strategy seems to be highly recommended for the safe operation of bearings subjected to high loads and load angles deviated from 90°.