In the present paper, the algorithm proposed by Giacopini et. al. [1], based on a mass-conserving formulation of the Reynolds equation using the concept of complementarity is suitably extended to include the effects of compressibility, piezoviscosity and shear-thinning on the lubricant properties. This improved algorithm is employed to analyse the performance of the lubricated small end and big end bearings of a connecting rod of a high performance motorbike engine. The application of the algorithm proposed to both the small end and the big end of a con-rod is challenging because of the different causes that sustain the hydrodynamic lubrication in the two cases. In the con-rod big end, the fluid film is mainly generated by the relative high speed rotation between the rod and the crankshaft. The relative speed between the two races forms a wedge of fluid that assures appropriate lubrication and avoids undesired direct contacts. On the contrary, at the con-rod small end the relative rotational speed is low and a complete rotation between the mating surfaces does not occurs since the con-rod only oscillates around its vertical axis. Thus, at every revolution of the crankshaft, there are two different moments in which the relative rotational speed between the con-rod and the piston pin is null. Therefore, the dominant effect in the lubrication is the squeeze caused by the high loads transmitted through the piston pin. In particular both combustion forces and inertial forces contribute to the squeeze effect. This work shows how the formulation developed by the authors is capable of predicting the performance of journal bearings in the unsteady regime, where cavitation and reformation occur several times. Moreover, the effects of the pressure and the shear rate on the density and on the viscosity of the lubricant are taken into account.

The Reynolds equation plays an important role for predicting pressure distributions for fluid film bearing analysis, One of the assumptions on the Reynolds equation is that the viscosity is independent of pressure. This assumption is still valid for most fluid film bearing applications, in which the maximum pressure is less than 1 GPa. However, in elastohydrodynamic lubrication (EHL) where the lubricant is subjected to extremely high pressure, this assumption should be reconsidered. The 2D modified Reynolds equation is derived in this study including pressure-dependent viscosity, The solutions of 2D modified Reynolds equation is compared with that of the classical Reynolds equation for the ball bearing case (elastic solids). The pressure distribution obtained from modified equation is slightly higher pressures than the classical Reynolds equations.

In many tribological applications, such as journal bearings and gears, a fluid film is used to accommodate velocity between moving surfaces. To model the behavior of this film and to predict its ability to carry load, the Reynolds equation is predominantly employed. As computational processing power continues to increase, computational fluid dynamics (CFD) is increasingly being employed to predict the fluid behavior in lubrication environments. Using CFD is advantageous in that it can provide a more general approximation to the Navier-Stokes equations than the Reynolds equation. Moreover, using CFD allows for the simulation of multiphase flows as could occur during bearing contamination and bearing exit conditions. Because the bearing surfaces move relative to each other as they obtain equilibrium with the fluid pressure, there is a need to incorporate the moving boundary into the CFD calculation, which is a non-trivial task. In this work, a fluid-structure interaction (FSI) technique is explored as an approach to model the dynamic coupling between the moving bearing surfaces and the lubricant. The benefits of using an FSI approach are discussed and the results of its implementation in a lubricated sliding contact model are presented.

Friction and wear behavior of lubricated sliding contact is determined by the operating lubrication regime. A useful approach to determining the operating lubrication regime is the calculation of the λ ratio, which is defined as the ratio of lubricant fluid film thickness (h), and the composite surface roughness (ơ) of contacting surfaces (λ = h/ơ). Thin-film tribological coatings are increasingly being used for application in lubricated machine elements such as gears and bearings. It is usually assumed by design engineers that application of thin-film coatings has no effect on fluid-film lubrication. This paper presents our experimental investigation of the impact of several (5) commercially available coatings on lubrication regime during a unidirectional sliding contact. Using a ball-on-flat contact configuration and lubricated with PAO basestock oil, tests were conducted in which the λ ratio was varied as a function of time, for both uncoated and coated flat specimen. In test with uncoated flat, the various distinctive lubrication regime of hydrodynamic, mixed and boundary were observed as indicated by the measured friction coefficient (Stribeck Curve). In tests with some of the coatings, especially the carbon based DLCs, there was no obvious distinctive transition in lubrication regime. In other coatings (ex. TiCN), various lubrication regime were also observed; although the rate of transition from one regime to the other was different. The effects of coatings are attributed to their inherent mechanical and tribological properties as well as their impact on the run-in process.

This application study of a swash-plate type axial piston pump was concerned about the hydrostatic lubrication characteristics of cylinder barrel and valve plate which are main rotating body and its opposite moving part respectively. A computer simulation was implemented to assess thrust bearing and mechanical sealing functions of the fluid film between cylinder barrel and valve plate. A new algorithm was developed to facilitate simultaneous calculations of dynamic cylinder pressure, 3 degree-of-freedom barrel motions considering inertia effect, and fluid film pressure assuming full fluid film lubrication regime. Using the simulation tool, force and moment balancing of cylinder barrel which is a key issue of piston pump design was analyzed. Time dependent fluid film pressure and thickness distributions for several given balance ratios were calculated. This analysis helps to decide appropriate balance ratio in the valve and cylinder barrel. Oil leakage flow and friction torque in the fluid film between cylinder barrel and valve plate were calculated as well and discussed in the viewpoint of energy loss. The results show that film thickness in plain surface is not high enough to bear the barrel and reduce power loss and that surface waviness which exists in actual sliding surfaces can have a positive effect on it. This simulation tool could also predict time dependent barrel motions due to simultaneous calculation algorithm. It has been known that cylinder barrel rotates with oscillation. Therefore average clearance, tilt angle, and azimuth angle were calculated for each time step and the results were discussed.

State of the art of hydrodynamic journal bearing lubrication is realized by a significant oversupply with lubricant, causing energy losses due to fluid film friction in the unloaded areas of the bearing. Reducing the lubricant flow however may lead to overheating or collapse of the load carrying fluid film, both resulting in a complete failure of the journal bearing. A new approach to safely reduce the lubricant flow is presented in this paper, by using a broadband piezoelectric acoustic emission sensor to detect ultrasonic structure-borne noise, usually caused by metal-to-metal contact at boundary conditions. The method of structure-borne noise analysis has proven to be suitable for detecting the occurrence of solid friction [1–4]. By combining structure-borne noise analysis with a closed loop control of a proportional flow control valve a condition dependent lubricant flow can be set. Thus lubricant friction in the bearing is reduced and additionally electrical energy in the peripheral devices, such as pumps can be saved.

In order to reduce friction losses and vibrations in main engine bearings, fluid film lubrication is combined to controllable radial oil injection. This work evaluates different geometric hybrid bearing configurations and control pressure rules for applying radial oil injection in main engine bearings of internal combustion engines. The conventional hydrodynamic lubrication ( CHL ) is combined with hydrostatic lubrication which is actively modified by radially injecting oil at controllable pressures, through orifices circumferentially located around the bearing surface. The behaviour of a main bearing of a medium size combustion engine, operating with radial oil injection and with four different control strategies is analyzed, giving some insights into the minimum fluid film thickness ( OFT ) and reduction of viscous friction losses. The behaviour of such parameters is compared to the case when the bearing operates with conventional hydrodynamic lubrication.

This paper presents a study of cavitation effects associated with the performance of fluid-film journal bearings subjected to fully-reversing sinusoidal loading. Employing an established mass-conserving cavitation algorithm, it is observed that periodic time histories of journal eccentricity and maximum film pressure are strongly influenced by the process of cavitation formation and collapse. Good agreement of predicted and experimental results is obtained over a large range of loads for cavitation threshold pressure values typically associated with vapor cavitation.

Fluid film bearings are widely used for high speed rotating machineries acting as rotating shaft support element. Especially, the bearings are widely applied to the OA equipments and IT devices. Optimization of bearing parameters is effective to improve the performance of the fluid film bearings since low noise and impact-proof characteristics are essential requirements for these equipments. On the other hand, bearings for miniaturized spindles are generally made by mass production process which will eventually requires reduction of production costs. In this paper, therefore small size HDD spindle using fluid film bearings is treated. Sensitivity analysis and optimum design that considered dimensional tolerances using the probabilistic techniques are conducted. As a result, the influence of bearing characteristic values on the occurrence of dimensional tolerances was clarified.

In the manufacturing process of small size fluid film bearings, the machining errors of groove affect the bearing characteristics. This paper describes the optimum design of small size fluid film thrust bearings to reduce the characteristics variability caused by some productivity. Firstly, from the original result of the modified spiral bearing obtained by the geometrical optimization, critical bearing parameters related to sensitivity of dynamic stiffness was investigated. From the sensitivity analysis, it was clarified that the parameters of groove depth and groove ratio have high sensitivity towards bearing stiffness. In the optimum design with consideration of productivity, errors for groove depth and groove ratio were given using probability theory with restriction towards the dynamic stiffness variability. From the results, the reduction of dynamic stiffness variability was accomplished. Furthermore, even if the manufacturing errors exist, the optimized bearing is operated safely without contact because it is able to stay in the range of the allowable film thickness.

The purpose of this paper is to present the experimental evaluation of the stiffness and damping coefficients of a pair of elastic rings used to support a fluid film bearing into a turbojet engine body. The experimental rig, the method of analysis and the experimental data are presented.

This study focuses on the thermohydrodynamic lubrication analysis of fluid film bearings with step on the surface such as a Rayleigh step bearing. In general, the Reynolds equation does not satisfy the continuity of the fluid velocity components at steps. This discontinuity results in the difficulty to solve the energy equation for the lubricants, because the energy equation needs the velocity components explicitly. The author has solved this problem by introducing the equivalent clearance height and the equivalent gradient of clearance height at steps. These parameters remove the discontinuity of velocity components and the energy equation as well, so that one can solve these equations on all of the bearing surfaces including the step region by finite differential method (FDM). The numerical results of pressure and temperature distributions by the proposed method for a Rayleigh step bearing were compared with the results obtained by a commercial CFD package. These results showed good agreement with each other. This method is extended to 2D unequal grid problems.

The effect of angular misalignment of plain journal bearings on the oil whirl and oil whip phenomena was investigated using a test rig comprising a flexible one inch diameter shaft supported on two cylindrical fluid film bearings. A matrix of experiments was designed where a precisely controlled angular misalignment between the shaft and the drive end, the non-drive end, or both bearings was induced. In each case we measure the onset of oil whirl and/or the onset of oil whip and the maximum speed that the test rig can reach before reaching a maximum vibration displacement of 1 mm at the location of the displacement sensor. The results show clearly that the angular misalignment of the bearings with respect to the shaft help delay the onset of oil whip from 3200 rpm to 4500 rpm in some cases. An interesting and new observation was the effect of the configuration of the misalignment on the overall stability characteristics. In particular, when the two bearings were misaligned in the same direction such that the two misaligned bearing planes were parallel to each other the onset of instability was more delayed and the overall operation was smoother.

This article deals with the finite differential method of static performance of a foil journal gas bearing. A foil bearing is a self acting hydrodynamic device, which separates stationary and rotating components of high speed rotating machinery by a fluid film of air or other gaseous lubricant. The present work concentrates on common approach in foil bearing in calculating the carrying capacity for a given shaft position (figure-1). During this work the external load is fixed and related shaft position is investigated. For steady operating characteristics such as minimum film thickness and load capacity predicted for the foil bearing. The system of governing equation is solved numerically with FDM by a computer program written in the MATLAB computing environment. A generalized hydrodynamic analysis is conducted to systematically analyses the effect like bearing speed is discussed.

The friction characteristics of lubricated contacts are usually determined by the shearing of three interfacial structural elements; namely lubricant fluid film, tribochemical reaction films and the near-surface materials. The shear behavior of the fluid film components of lubrication can be adequately described by either the hydrodynamic, or elastohydrodynamic theories and calculations. The shear behavior of the near surface materials can also be approximated by contact mechanics. However, due to the complexity and lack of adequate information, description and analysis of the tribochemical film contributions to frictional behavior is more challenging. In this study we present evaluation of the friction behavior of a lubricated contact as a function of tribological test duration, as the tribochemical surface films were being formed. Tests were conducted with two different formulated lubricants, in addition to an unformulated PAO basestock lubricant. One of the formulated lubricants consists of PAO synthetic basestock with 2.5% each of ZDDP and MoDTC additives. The other formulated lubricant is a fully formulated commercial gear oil with similar viscosity. During the friction tests in a fully flooded reciprocating sliding roller-on-flat contact configuration, the friction coefficient decreased exponentially as the tribochemical films were formed; highlighting the impact of boundary films on friction. In the test with the basestock fluid, the friction remained constant for the duration of the test; although an oxide layer was formed. Nanoindentation hardness and modulus measurements were conducted on two of the tribochemical films to measure their mechanical properties and the consequent impact on measured friction during testing.

Advanced closed loop power generation cycles are under consideration for a variety of terrestrial and aerospace power systems [1]. High pressure closed brayton cycles (CBC) and supercritical cycles (SCS) offer an advantage where the cycle working fluid can also be used as the lubricant for the fluid film bearings that support the high speed turbomachinery. Unfortunately the use of supercritical carbon dioxide as a lubricant is not well understood. In the supercritical condition fluids that are typically thought of as ideal gases take on a significantly different characteristic. While these fluids typically maintain gas-like absolute viscosities, their densities are liquid like. The combination of these effects leads to the emergence of inertial effects in fluid film bearings. In addition to the inertial effects that are brought on by the high fluid density, the temperature of the lubricant cannot be controlled independently of the thermodynamic process. This situation leads to technical challenges in maintaining dimensional stability and clearance control between the rotating and stationary surfaces of the bearings.

An oil lubricated wave bearing has been tested on a new rig for fluid film journal bearings at NASA Glenn Research Center in Cleveland, Ohio, USA. The tests are intended to evaluate the rig possibilities of running without misalignment. Data recorded under steady-state conditions included oil flow rate, input, output and oil supply temperatures, and shaft position. Two sets of data were collected: i) by varying the load to 9000 N at a constant shaft rotation speed of 8,000 RPM and ii) by varying the speed from 9,000 to 12,000 RPM at constant load of 6,700 N. The temperatures of the metal sleeves were also recorded. Vibration levels at four locations were displayed and recorded. These measurements indicated that damping from the wave bearings provides significant attenuation of the vibration generated by the air turbine that drives the rig.

The present work deals with the application of the Lattice Boltzmann Method (LBM), which is a relatively new Computational Fluid Dynamics approach, to fluid film lubrication. LBM accounts for the inertia forces, while being easier to implement than Navier-Stokes solvers for complex geometric configurations. The LBM solution for a classic case is presented in comparison with the analytic Reynolds solution and the numeric solution obtained with Navier-Stokes solvers.

A dimensionless theoretical model of Soft Elasto Hydrodynamic Lubrication (SEHL) between partially textured elastomer and rigid counterpart is developed. The model consists of a soft elastomer with partial Laser Surface Texturing (LST) and an absolutely rigid and smooth counterpart moving relatively to each other in the presence of viscous lubricant. The elastomer surface is partially textured at its leading edge in the form of spherical micro-dimples. The pressure distribution in the fluid film and the elastic deformations of the elastomer are obtained from a simultaneous solution of the Reynolds equation and the equation of linear elasticity, respectively. Friction force and load carrying capacity are evaluated by integration of the shear stress and pressure fields in the viscous fluid film, respectively. The main goal of the present work is to study the potential of the elastomer partial LST in SEHL to friction reduction.

This work describes in details the steps involved within the mathematical modelling of multibody systems (rigid and flexible) interconnected via controllable thin fluid films. The dynamics of the mechanical components are described with help of multibody dynamics and finite element method. In this paper, the methodology is applied to reciprocating machines such as hermetic reciprocating compressors and internal combustion engines. In previous studies [1], it has been shown that for a light duty vehicle, the friction losses may reach until 48% of the total energy consumption of an engine and from that, almost 30% are coming from bearings and crankshaft. Therefore, considering that the dynamics of the fluid films in the journal bearings can be actively controlled by means of different types of actuators, allowing significant reduction of wear and vibrations, one of the aims of this paper is to study the feasibility of applying active lubrication to the main journal bearings of reciprocating machines. In this framework the paper gives a theoretical contribution to the combined fields of fluid-structure interaction and active vibration control. The hydrodynamic pressure distribution for an active lubricated finite journal bearing dynamically loaded can be calculated by numerically solving the modified Reynold’s equation [2], by means of finite-difference method and integrated over the pressure area in order to obtain the dynamic reaction forces among components. These forces are strongly nonlinear and dependent on the relative kinematics of the system. From the point of view of active lubrication and specifically considered the case of a dynamically loaded journal bearing, the injection pressure should be controlled in the time domain. However, taking into account that the pressures and reaction forces in a reciprocating machine have a cyclic behaviour, the fluid film thickness of the main bearings may be modified by controlling the oil pressure injection, depending on the crank angle and the load bearing condition. It can be mentioned that the pressure and flow may be controlled by mechanical cam systems, piezoelectric nozzles [3] [4] or servovalves [5] [6], therefore, an adequate control strategy has to be defined. The fluid film forces are coupled to the set of nonlinear equations that describes the dynamics of the mechanical system. Such a set of equations is numerically solved giving some insights into the following parameters: a) maximum fluid film pressure, b) minimum fluid film thickness, c) maximum vibration levels and d) viscous frictional forces. The behaviour of such parameters is investigated when the system operate with conventional hydro-dynamic lubrication, passive hybrid lubrication and controlled hybrid lubrication.