Research Papers: Applications

J. Tribol. 2009;132(1):011101-011101-6. doi:10.1115/1.4000271.

This paper deals with vibrations and acoustic emissions (AEs) of linear-guideway type recirculating ball bearings with a millimeter-sized artificial defect in the carriage. The vibration and AE of one normal bearing without a defect (Type N), and six defective bearings (Types D1–D6) were measured using a linear velocity of 1 m/s. The defects in the bearings range from 1.87 mm to 6.77 mm in length, 2.45 mm to 3.80 mm in width, and 23.3μm to 68.0μm in depth. The experimental results show that the pulse amplitudes of the vibrations and AE (both the peak-to-peak and RMS values) of the defective bearings have a tendency to be greater than those of the normal bearing. Both the measured vibration and AE components over 30 kHz increased in the carriages with defects. To explain these increases in the defective bearings, a collision model with balls and one defect in the carriage is presented. That collision model shows that the increases in both the vibrations and AE of the defective bearings are caused by increases in the defect angle. A reasonable correlation exists between the presented collision model and the measured vibrations or AE of the defective bearings.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;132(1):011102-011102-9. doi:10.1115/1.4000277.

This article deals with the vertical stiffnesses of preloaded linear guideway type ball bearings (linear bearings) incorporating the flexibility of the carriage and rail. First the vertical stiffnesses of light and medium preloaded linear bearings were measured, as well as the outward carriage deformations in the width direction. Compared with the stiffnesses calculated by the conventional rigid model (assuming the carriage and rail are rigid, except for the contact points with the balls), the measured stiffnesses were about 40% less. In preloaded linear bearings under a vertical load, the side faces of the carriage deformed outward. The deformations were minimal at the top, increased toward the bottom, and had a tendency to be greater under either a larger preload or a smaller vertical load. The measured stiffnesses and outward carriage deformations cannot be explained using the conventional rigid model. To overcome these problems with the conventional rigid model, a flexible model (taking into account the flexibility of the carriage and rail) is presented in this article. The flexible model deformations were estimated through finite element (FE) analysis. The Hertzian contacts between the balls and the carriage or rail also were considered. With relative errors of 9–21%, the calculated stiffnesses using the flexible model more closely matched the measured stiffnesses. Also, the calculated outward carriage deformations matched the measured deformations well. Clearly, there is a better match between the calculated results of the flexible model and the measurements than with the conventional rigid model.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;132(1):011103-011103-7. doi:10.1115/1.4000545.

Inertial effects due to the centripetal forces may become dominant at high rotational speeds in hydrostatic thrust bearings. Although this influence has been recognized in literature, bearings are commonly optimized with respect to the minimum friction, and the dissipation function has not been taken into account in the optimization procedures. It is observed that the secondary flow caused by the inertia term gives a large contribution to the dissipation for applications with a high rotational speed. In this study, the minimum dissipation for annular and circular recess thrust bearings operating at a certain rotational speed is determined by finding the optimum film thickness in the recess. An example is given for annular recess thrust bearings.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;132(1):011104-011104-7. doi:10.1115/1.3195037.

In a disengaged or open clutch mode, one plate rotates while the other is stationary. This speed difference between the two plates (on the order of 1000 rpm) and the small clearance between them (on the order of 100μm) results in large velocity gradients. Transmission fluid is passed between clutches since during reengagement; this oil provides lubrication and carries heat away. However, during the disengaged mode the shearing of this oil as it passes between the plates results in viscous drag that wastes power. Introduction of air between the two plates during the disengaged mode, referred to as aeration, is the most significant way of reducing this friction drag due to low viscosity of air compared with oil. Open clutch drag reduction is enhanced by providing grooves on one of the plates since they are known to promote aeration. Yet, a continuous supply of lubrication oil is necessary, even during disengagement. This study examines the underlying processes responsible for the oil flow between grooved disks and possible aeration through a combination of experiments and numerical computations. A two-dimensional model of the three-dimensional, single-phase flow between a stationary and a rotating clutch plate is presented, which is capable of describing pressures and shear stress distribution for plates with radial grooved geometries. The computational fluid dynamics code FLUENT ® is used to examine the single-phase and aerated flows between the plates. These results are compared with accompanying experimental observations. We also examine new groove designs to study their efficiency in promoting aeration. Finally, we propose reasons for grooves promoting aeration in clutches.

Commentary by Dr. Valentin Fuster

Research Papers: Biotribology

J. Tribol. 2009;132(1):011201-011201-8. doi:10.1115/1.4000278.

Human ankle joint lubrication in walking is analyzed. A biphasic mixture model is considered for articular cartilage (ideal interstitial fluid and elastic porous matrix that is transversely isotropic and inhomogeneous throughout its thickness). Synovial fluid is considered Newtonian. Its viscosity is due to the macromolecules of hyaluronic acid that are too large to enter the matrix pores. Due to the fluid pressure gradient water and small solutes pass through the matrix pores and across the articular surface in both directions. The effect of the time varying concentration of hyaluronic acid or of the synovial fluid viscosity on the synovial film thickness distribution is small and neglected in the model. Periodic sliding motion of the articular surfaces and periodic loading of the joint as encountered in walking are included in the analysis. Synovial fluid serves as a fluid lubricant. The model shows that soon after the onset of walking the normal human ankle joint works in a mixed lubrication mode (a combination of boundary and fluid-film lubrications). A protective gel layer formed in the gap due to the synovial fluid filtration by cartilage may serve as a boundary lubricant. The synovial gel layer is not guaranteed in the osteoarthritic case, and the rough sliding surfaces may get repeatedly into an intimate contact and wear off due to the reciprocating sliding motion.

Commentary by Dr. Valentin Fuster

Research Papers: Contact Mechanics

J. Tribol. 2009;132(1):011401-011401-7. doi:10.1115/1.4000305.

A general contact stiffness model is proposed in this paper to study the contacts between rough surfaces of machined plane joints. The proposed model uses fractal geometry for surface topography description, elastic-plastic deformation of contacting asperities, and size-dependent contact stiffness of microcontacts, where the contact stiffness is derived from Hertz contact theory. Three cast iron specimens are produced from different machining methods (milling, grinding, and scraping), and their rough surface profiles are extracted. The structure function method was used to calculate each profile’s fractal dimension and scale coefficient. Both theoretical analysis and experimental results of contact stiffness are obtained for these specimens under different contact loads. The comparison between the theoretical contact stiffness and the experimental results at the interface indicates that the present fractal model for the contact stiffness is appropriate and the theoretical contact stiffness is consistent with the experimental data.

Commentary by Dr. Valentin Fuster

Research Papers: Elastohydrodynamic Lubrication

J. Tribol. 2009;132(1):011501-011501-9. doi:10.1115/1.4000270.

In this study, a transient, non-Newtonian, mixed elastohydrodynamic lubrication (EHL) model of involute spur gear tooth contacts is proposed. Unlike the contact between two cylindrical rollers, spur gear contacts experience a number of time-varying contact parameters including the normal load, radii of curvature, surface velocities, and slide-to-roll ratio. The proposed EHL model is designed to continuously follow the contact of a tooth pair from the root to the tip to capture the transient characteristics of lubricated spur gear contacts due to these parameter variations, instead of analyzing the contact at discrete positions assuming time-invariant parameters. The normal tooth force along the line of action is predicted by using a gear load distribution formulation and the contact radii and tangential surface velocities are computed from the kinematics and geometry of involute profiles. A unified numerical approach is adapted for handling asperity interaction in mixed EHL conditions. The differences between the transient and discrete EHL analyses are shown for a spur gear pair having smooth surfaces and different tooth profile modifications. The transient behavior predicted by the proposed model is found to be mainly due to the squeezing and pumping effects caused by sudden load changes. The lubrication behavior under rough conditions is also investigated at different operating conditions.

Commentary by Dr. Valentin Fuster

Research Papers: Friction & Wear

J. Tribol. 2009;132(1):011601-011601-7. doi:10.1115/1.4000273.

In the present investigation, a tip test based on upsetting and backward extrusion was utilized to characterize the effect of surface roughness of the billet and forming tools, and the type of lubricants on friction. For the test, cylindrical specimens made of aluminum alloys of 6061-O and 2024-O, and single punch and two die sets with different surface topologies, were used with four lubricants such as VG32, VG100, corn oil, and grease. The load levels and tip distances were measured for both materials, and compared with each other to determine shear friction factors at the punch and counter punch interfaces separately, depending on the variation in surface topologies and lubrications using finite element simulations. As a result, a linear relationship among the dimensionless load, tip distance, and shear friction factors at the punch and counter punch interfaces was derived for the experimental conditions investigated. The slope change of this linear relationship from negative to positive clearly depends on the variation in surface conditions at the billet/punch and billet/counter punch interfaces. Also, it was demonstrated that the dimensionless tip distance for the frictionless case can be extrapolated from the experimental data. This value can be used for characterizing the relative effect on friction due to surface conditions at the punch and counter punch, and lubrication quality of the lubricant for the given processing conditions.

Commentary by Dr. Valentin Fuster

Research Papers: Hydrodynamic Lubrication

J. Tribol. 2009;132(1):011701-011701-11. doi:10.1115/1.4000279.

An engineered thermal management is fundamental to the application of gas foil bearings (GFBs) as turboshaft supports in rotorcraft propulsion systems. The paper presents a model for the thermal energy transport in a rotor-GFB system operating at high temperature with typical inner and/or outer cooling flows. Predicted film temperatures agree with published test data, demonstrating the effectiveness of an outer cooling stream to remove heat and to control the operating temperature. The inner flow stream is not as efficient. The analysis shows paths of thermal energy by conduction and convection to assist in the design and troubleshooting of rotor-GFB systems operating hot. Bearing temperatures and shaft motions measurements are obtained in a test rotor electrically heated to 132°C. In speed-up tests to 26 krpm, the rotor motion amplitude drops suddenly just above the critical speed, thus, evidencing the typical hardening of compliant bearings. At the hottest test condition, since air is more viscous, the rotor peak motion amplitude decreases, not showing a jump. The coastdown tests show the critical speed increases slightly as the temperature increases.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;132(1):011702-011702-13. doi:10.1115/1.4000280.

Misalignment affects nearly all the bearing performance parameters including the cavitation, thermal field, leakage flow-rate, and moments. The present paper provides a comprehensive analysis of misaligned journal bearings based on a three-dimensional mass-conservative thermohydrodynamic model that appropriately takes into account the film rupture and reformation. An extensive set of numerical solutions are presented to closely examine the effects of misalignment in journal bearings.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;132(1):011703-011703-7. doi:10.1115/1.4000269.

This paper describes the stabilization method for small-bore circular journal bearings using starved lubrication. First, we describe the experimental examination to confirm the effect of supply oil conditions on stability of circular journal bearing by using a high-speed test rig. Then, the theoretical model considering the effect of amount of supply oil is discussed. Journal center trajectories are calculated by nonlinear motion analysis under various conditions. The theoretical results agree well with the experimental ones for three types of supply oil conditions and the mechanism of the stabilization by using the starved lubrication for small-bore journal bearings is clarified. Moreover, we suggest a supply oil control mechanism to stabilize the journal bearing using starved lubrication. Finally, the effectiveness of the proposed control mechanism on stability for high-speed small-bore journal bearings is verified experimentally.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;132(1):011704-011704-8. doi:10.1115/1.4000515.

Journal misalignment exists generally in journal bearings. When severe journal misalignment takes place, the minimum film thickness of journal bearings reduces greatly. In this condition, the surface roughness, the oil viscosity-pressure relationship (VPR), and the thermal effect have obvious effects on hydrodynamic lubrication performance of misaligned bearings. In this paper, the oil film pressure, oil film temperature, load-carrying capacity, end leakage flow rate, frictional coefficient, and misalignment moment of a journal bearing with different angles of journal misalignment and surface roughness, and considering oil VPR and thermal effect, were calculated based on the generalized Reynolds equation, energy equation, and solid heat conduction equation. The results show that the oil VPR and surface roughness have a significant effect on the lubrication of misaligned journal bearings under large eccentricity ratio. The thermal effect will affect obviously the lubrication of misaligned journal bearings when eccentricity ratio and angle of journal misalignment are all large. In the present design, the size of the journal bearing is compact more and more, and the eccentricity ratio and angle of journal misalignment are usually large in operating conditions. Therefore, it is necessary to take the effects of journal misalignment, surface roughness, oil VPR, and thermal effect into account in the design and analyses of journal bearings.

Commentary by Dr. Valentin Fuster

Research Papers: Lubricants

J. Tribol. 2009;132(1):011801-011801-9. doi:10.1115/1.4000274.

A model for oil-in-water emulsion has been developed in this paper. A group of viscosity coefficients transiting smoothly and incessantly from the thick film region to the thin film region is defined. The contributions from disperse and continuous phases to the total lubricant pressure and pressure gradient are functions of the oil concentration and the film thickness. The parameters used in these functions are determined by a series of computational fluid dynamics simulations. The onset of inversion and the viscosity after inversion are also investigated. It is found that the critical volume fraction of oil in the inception of inversion is dependent on the oil viscosity and a factor regarding the combined effects from the emulsifier, pH value, droplet size, and the shear rate. A series of simulations using the proposed model has been carried out and compared with the experimental results, such as the film thickness and the extension of oil pool for various rolling speeds and supply oil concentrations. The numerical outputs are basically in agreement with the experiments.

Commentary by Dr. Valentin Fuster

Research Papers: Magnetic Storage

J. Tribol. 2009;132(1):011901-011901-11. doi:10.1115/1.4000514.

Near or partial contact sliders are designed for the areal recording density of 1Tbit/in.2 or even higher in hard disk drives. The bouncing vibration of an air bearing-slider in near or partial contact with the disk is numerically analyzed using three different nonlinear slider dynamics models. In these three models, the air bearing with contact is modeled either by using the generalized Reynolds equation modified with the Fukui–Kaneko slip correction and a recent second order slip correction for the contact situation, or using nonlinear springs to represent the air bearing. The contact and adhesion between the slider and the disk are considered either through an elastic contact model and an improved intermolecular adhesion model, respectively, or using an Ono–Yamane multi-asperity contact and adhesion model (2007, “Improved Analysis of Unstable Bouncing Vibration and Stabilizing Design of Flying Head Slider in Near-Contact Region  ,” ASME J. Tribol., 129, pp. 65–74.). The contact friction is calculated by using Coulomb’s law and the contact force. The simulation results from all of these models show that the slider’s bouncing vibration occurs as a forced vibration caused by the moving microwaviness and roughness on the disk surface. The disk surface microwaviness and roughness, which move into the head disk interface as the disk rotates, excite the bouncing vibration of the partial contact slider. The contact, adhesion, and friction between the slider and the disk do not directly cause a bouncing vibration in the absence of disk microwaviness or roughness.

Commentary by Dr. Valentin Fuster

Research Papers: Mixed and Boundary Lubrication

J. Tribol. 2009;132(1):012101-012101-9. doi:10.1115/1.4000272.

A simple but realistic dynamic friction model for the lubricated sliding contact is developed based on decoupling the steady and unsteady terms in Reynolds equation. The model realistically captures the physics of friction behavior both when speed is increased unidirectionally or when operating under oscillating condition. The model can simulate the transition from boundary to mixed to full film regimes as the speed is increased. Two different classes of simulations are performed to show the utility of the model: the so-called quasisteady, where the sliding velocity is varied very slowly, and the oscillating sliding velocity, where the friction coefficient exhibits a hysteresis type behavior. Both categories of simulation are verified by comparing the results with published experimental data.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;132(1):012102-012102-8. doi:10.1115/1.4000306.

This paper presents a simple approach to predict the behavior of friction coefficient in the sliding lubricated point contact. Based on the load-sharing concept, the total applied load is supported by the combination of hydrodynamic film and asperity contact. The asperity contact load is determined in terms of maximum Hertzian pressure in the point contact while the fluid hydrodynamic pressure is calculated through adapting the available numerical solutions of elastohydrodynamic lubrication (EHL) film thickness formula for smooth surfaces. The simulations presented cover the entire lubrication regime including full-film EHL, mixed-lubrication, and boundary-lubrication. The results of friction, when plotted as a function of the sum velocity, result in the familiar Stribeck-type curve. The simulations are verified by comparing the results with published experimental data. A parametric study is conducted to investigate the influence of operating condition on the behavior of friction coefficient. A series of simulations is performed under various operating conditions to explore the behavior of lift-off speed. An equation is proposed to predict the lift-off speed in sliding lubricated point contact, which takes into account the surface roughness.

Commentary by Dr. Valentin Fuster

Technical Briefs

J. Tribol. 2009;132(1):014501-014501-7. doi:10.1115/1.4000276.

In this paper, pressure and shear stress are derived under steady state using one-dimensional analysis of the single-grooved slider bearing and journal bearing with partial slip on the stationary surface. The Reynolds boundary conditions are used in the analysis of journal bearing to predict the extent of the full film region. In the cases of partial slip slider and journal bearing, the pressure distribution is higher compared with the conventional bearing with no slip. In the case of partial slip on both slider and journal bearing surfaces, the single-groove, immediately followed by the partial slip region, results in the increase in pressure distribution. The results also show that in comparison to the conventional bearing with no slip, in the cases of partial slip slider and journal bearing, the shear stress increases before the region of slip/no slip interface, while the shear stress decreases in the region of no slip. In the case of the partial slip region on bearing surfaces, the shear stress distribution is lower in the region immediately after the groove. Significant pressure distribution is obtained due to the influence of partial slip on the slider bearing with uniform film thickness and the concentric journal bearing. The maximum pressure occurs at the end of the region of groove, immediately followed by the region of the partial slip. It is found that the pressure distribution of the slider and journal bearing with partial slip surface are not influenced with the further increase in the nondimensional slip coefficient (A) from 10 to 100.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;132(1):014502-014502-9. doi:10.1115/1.4000389.

A new method for determining a closed-form expression for the hydrodynamic forces in finite-length plain journal bearings is introduced. The method is based on applying correction functions to the force models of the infinitely long (IL) or infinitely short (IS) bearing approximation. The correction functions are derived by modeling the ratio between the forces from the numerical integration of the two-dimensional Reynolds equation and the forces from either the IL or IS bearing approximation. Low-order polynomial models, dependent on the eccentricity ratio and aspect ratio, are used for the correction functions. A comparative computational study is presented for the steady-state behavior of the bearing system under static and unbalance loads. The results show the proposed models outperforming the standard limiting approximations as well as a model based on the finite-length impedance method.

Commentary by Dr. Valentin Fuster


J. Tribol. 2009;132(1):015501-015501-1. doi:10.1115/1.4000307.

The authors observed that the strength of triboemission, for diamond-Si and diamond-Ge pairs, decreased as contact progressed over the same wear track. Nakayama and Fujimoto (1) observed similar tendencies although accompanied by occasional high strength emission peaks. Nakayama and Fujimoto proposed that the weak signals are due to their samples being mono-crystalline silicon, whereas they suggested that the strong signals are probably due to contamination of samples by formation of oxides during pre-experimental surface preparation in air. This author suggests that the observed triboemission behavior in the present work and the work of Nakayama is a consequence of a pressure-induced metallization of silicon. Repeated passing of the diamond stylus on the same wear track, under suitable conditions, would induce metallization (2). Such a notion is supported by the observation of plastically extruded silicon plastically extruded silicon (PES) along the wear track (3). The presence of PES suggests a pressure induced semi-conductor-to-metal phase transformation, i.e., the formation of the metallic phase Si-II (β-tin) which has low electrical resistivity (4). This low electrical resistivity can explain the observed emission behavior. For mono-crystalline silicon transformation from Si-I to the metallic phase Si-II takes place in the pressure range 8.5 GPa <P< 12 GPa. Using 1200 GPa and 110 GPa for the moduli of elasticity, 0.2 and 0.28 for Poisson's ratio for diamond and silicon, respectively, and considering the experimental conditions of Nakayama, calculation of the Hertzian contact stress yields a value of 9.6 GPa. This value favors a transition from the semi-conductor phase to a metallic phase. Further using the Johnson solution for pressure under a conical indenter considering the experimental conditions, reported by the current authors, we reach a similar conclusion.

Commentary by Dr. Valentin Fuster

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