J. Tribol. 2012;134(2):021101-021101-7. doi:10.1115/1.4006175.

An external load applied to a radial rolling bearing is distributed among the rolling elements. In many applications, the bearing internal load distribution may be altered by the elastic deformations of the bearing rings. This alteration can have an effect on bearing life. The objective of this study is to investigate the effect of load distribution on bearing life, both theoretically and experimentally, using several housing models which provide different contact conditions between the housing bore and the outer ring. This paper first presents a newly developed method of determining dynamic load distributions with an optical fiber strain sensor. The measurements of the load distribution for the housing models by using this method have shown that the contact condition between the housing bore and the outer ring affects the load distribution, and the effect of the load distribution on the bearing life has been confirmed by the theoretical calculation of the bearing life. Furthermore, endurance tests using dented bearings were performed to validate the effect of load distribution on bearing life. The results of the tests have substantiated that the bearing life is substantially affected by the load distribution; moreover, it has been shown that there is a linear relationship between the calculated lives and the experimental ones.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(2):021102-021102-9. doi:10.1115/1.4005951.

The internal load distribution in rolling bearings has a high impact on the bearing fatigue life. This study presents a method to optimize roller bearing housing design in order to maximize the bearing fatigue life by ensuring an optimal internal load distribution. An FE-model of a cylindrical roller bearing utilizing nonlinear springs in the roller modeling is presented, which is capable of simulating the bearing load distribution efficiently. The optimal load distribution is achieved by specifying the desired internal load distribution as design constraints in a topology optimization of the bearing housing design. The superiority of the method is clearly demonstrated through case studies involving a cylindrical roller bearing, where it is shown that the fatigue life is increased and the bearing housing mass and roller contact misalignment is reduced.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(2):021103-021103-13. doi:10.1115/1.4006135.

Rolling contact bearing life is calculated using stresses calculated at the surface and in the volume. Surface stresses account for profile and misalignment as well as asperity deformations. Sub-surface stresses are calculated beneath the asperities (for defining the life of the surface) and deeper in the volume for calculating the life of the volume. The stress-life criterion adopted is the Dang Van one in which the local stabilized shear stress is compared to the material endurance limit defined as a function of the hydrostatic pressure (itself a function of the contact pressure) but also residual stresses and hoop stresses (due to fit). A stress-life exponent c, of the order of 4 (instead of 34/3 in the standard Lundberg and Palmgren model) is used for respecting a local load-life exponent of 10/3 at typical load levels. Life of any circumferential slices of the inner, outer, and roller is defined for obtaining the final bearing life. Trends showing how the bearing life varies as a function of the applied bearing load and Λ ratio (film thickness/RMS roughness height) are given.

Topics: Stress , Pressure , Bearings
Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(2):021104-021104-8. doi:10.1115/1.4006136.

The stress based life model described in Paper I was calibrated using a large database of experimental results from a global quality audit test program as well as special development tests conducted for this validation effort. All tests used in the calibration of the new model were case carburized or through hardened tapered roller bearings. The initial model comparison to test results showed very good correlation with a median ratio of test life to calculated life very close to one. Higher accuracy of the stress based model compared to the traditional factor based method was also demonstrated by narrower confidence bands (less data scatter). Validation testing of case carburized tapered roller bearings as well as through hardened spherical roller bearings was also conducted under expanded test conditions beyond those utilized in the quality audit test program (i.e., high and low load, high and low λ, imposed misalignment, and heavy inner ring interference fits). Although the median ratio of relative life for the validation testing showed the stress based method to be conservative and well above one, the stress based method still showed better accuracy than the traditional factor based method as well as narrower confidence bands for this additional body of experimental data. The conservative results can be explained by use of high quality steel and manufacturing processes in a prototype facility and not series production equipment as was the case with the quality audit database.

Commentary by Dr. Valentin Fuster

Coatings & Solid Lubricants

J. Tribol. 2012;134(2):021301-021301-8. doi:10.1115/1.4005265.

The local yield maps for the identification of the yield initiation positions of hard coating on three-dimensional (3D) elastic half space under sliding contact were developed. In this study, the semi-analytical method (SAM), which is based on the conjugate gradient method (CGM) and the discrete convolution and fast Fourier transform (DC-FFT) technique, was employed to analyze the contact problem. By using this method, the von Mises stress distributions for various combinations of coating thicknesses, friction coefficients, and elastic moduli of the coating and substrate were calculated. Then, the positions of yield initiation were found with the calculated results by comparing the critical maximum contact pressure Pmax,c for von Mises yielding at or in the different positions (surface, coating, interface, and substrate), and the 3D-local yield maps were introduced in relation to the yield strength ratio of the coating to the substrate (Yf /Yb ) and the ratio of the coating thickness to the Hertzian contact radius (t/a0 ). Finally, the effect of critical friction coefficient on the transition of yielding positions was discussed.

Commentary by Dr. Valentin Fuster

Contact Mechanics

J. Tribol. 2012;134(2):021401-021401-8. doi:10.1115/1.4006296.

A 3D graded coating/substrate model based on multigrid techniques within a finite difference frame work is presented. Localized refinement is implemented to optimize memory requirement and computing time. Validation of the solver is performed through a comparison with analytical results for (i) a homogeneous material and (ii) a graded material. The algorithm performance is analyzed through a parametric study describing the influence of layer thickness (0.01 < t/a < 10) and mechanical properties (0.005 < Ec /Es  < 10) of the coating on the contact parameters (Ph , a). Three-dimensional examples are then presented to illustrate the efficiency and the large range of possibilities of the model. The influence of different gradations of Young’s modulus, constant, linear and sinusoidal, through the coating thickness on the maximum tensile stress is analyzed, showing that the sinusoidal gradation best accommodates the property mismatch of two successive layers. A final case is designed to show that full 3D spatial property variations can be accounted for. Two spherical inclusions of different size made from elastic solids with Young’s modulus and Poisson’s ratio are embedded within an elastically mismatched finite domain and the stress field is computed.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(2):021402-021402-9. doi:10.1115/1.4006248.

Revolute joints (also called pin joints or hinge joints) are used in many different mechanical systems such as robotic arms, door hinges, folding mechanisms, or hydraulic shovels. Since they transmit forces and give a rotational degree of freedom to the connected parts, revolute joints have a major impact on the dynamic behavior of the system into which they are built. Two main characteristics of these elements are their stiffness and their clearance. Both of them change as the wear between the joint’s pin and the rod hole increases during operation. In order to consider these aspects in a multibody simulation an analytical, numerically effective method has been developed to calculate the stiffness of a revolute joint in dependence of the geometry and the wear state. In addition, the calculation algorithm allows for for the analysis of the local friction energy that occurs in the contact zone. In this paper, the calculation approach is presented together with the results for two different steady loaded revolute joints.

Commentary by Dr. Valentin Fuster

Elastohydrodynamic Lubrication

J. Tribol. 2012;134(2):021501-021501-7. doi:10.1115/1.4005771.

The unified approach based upon the Reduced Reynolds technique is applied to develop a deterministic transient mixed lubrication line contact model. This model is used in spur gear applications to comprehensively show effects of roughness, working conditions, i.e., rotational speeds and loads on pressure ripples and severity of asperity contacts. Results show effects of the speed, the load, as well as the RMS value are coupled which makes it difficult to evaluate lubrication states by only considering one variable. Considering the Ree-Eyring non-Newtonian behavior could alleviate pressure ripples significantly, compared with the Newtonian fluid assumption. Small RMS values of surfaces, which could be achieved by superfinish techniques, would be desirable when evaluating gear tooth surface contact performances.

Commentary by Dr. Valentin Fuster

Hydrodynamic Lubrication

J. Tribol. 2012;134(2):021701-021701-7. doi:10.1115/1.4005264.

CoNiMnP permanent magnetic films have been electroplated into arrayed round dimples (with diameters from 100 μm to 700 μm) machined on the substrate surface (316 stainless steel). These films could be magnetized and could generate the arrayed micro-magnetic field. Compared with normal surfaces (316 stainless steel flat surfaces without any dimples or coatings), the frictional properties of such magnetic surfaces were investigated under different loads and sliding speeds when lubricated with ferrofluids using a friction test rig. Much attention was paid to the effect of the dimple sizes on the lubrication properties. In addition, the magnetic properties of the dimples arrayed surface were analyzed by finite element analysis software (Ansoft Maxwell 3D). The results show that there exists the optimized geometrical parameter of the arrayed magnetic surface, which displays the best tribological performance when lubricated with ferrofluids.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(2):021702-021702-9. doi:10.1115/1.4005217.

The cavitation bubble structures for the stationary specimen method were clarified for various distances, h, between the stationary specimen and the horn-tip surface. The generated cavitation bubbles constituted a huge number of tiny bubbles and bubble clusters of different sizes. The maximum cluster size was 1.4 mm. The observed cavitation patterns systematically changed during tests from the subcavitating state to the supercavitating state with respect to the separation distance, h. For h <4 mm, the bubbles have a definite trajectory, and the pressure patterns manifest a circular shape as a result of streaming induced by ultrasonic cavitation. The feature morphology of the eroded surfaces revealed that the predominant failure mode was fatigue. In the light of the material failure features and the cavitation patterns, it is also deduced that the important mechanism to transfer the cavitation energy to the solid is shock pressures accompanied by collapsing clusters.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(2):021703-021703-11. doi:10.1115/1.4006063.

In this study, a three-dimensional thermohydrodynamic (THD) CFD model is developed to study the characteristics of an inward pumping spiral groove mechanical seal pair using a commercial CFD software CFD-ACE + . The model is capable of predicting the temperature distribution and pressure distribution of the seal pair. Based on the CFD model, a parametric study is conducted to evaluate the performance of the seal. It is found that thermal behavior plays an important role in the overall performance of a seal. The spiral groove parameter can be optimized to achieve desired performance. The optimization is dependent on the application requirement of the seal.

Commentary by Dr. Valentin Fuster


J. Tribol. 2012;134(2):021801-021801-8. doi:10.1115/1.4005374.

The recent move toward physics-based elastohydrodynamics promises to yield advances in the understanding of the mechanisms of friction and film generation that were not possible a few years ago. However, the accurate correlation of the low-shear viscosity with temperature and pressure is an essential requirement. The Ashurst-Hoover thermodynamic scaling, which has been useful for thermal elastohydrodynamic simulation, is normalized here in a manner that maps the viscosity of three widely different liquids onto a master Stickel curve. The master curve can be represented by a combination of two exponential power law terms. These may be seen as expressions of different molecular interaction mechanisms similar to the two free-volume models of Batschinski-Hildebrand and Doolittle, respectively. The new correlation promises to yield more reasonable extrapolations to extreme conditions of temperature and pressure than free-volume models, and it removes the singularity that has prevented wide acceptance of free-volume models in numerical simulations.

Commentary by Dr. Valentin Fuster

Micro-Nano Tribology

J. Tribol. 2012;134(2):022001-022001-7. doi:10.1115/1.4005891.

This work deals with the effect of surface roughness parameters on the frictional properties of nanowire-based lubrication systems (NBLS) across Cu surfaces with various topographies. The friction coefficient was discussed in the context of surface roughness parameters including the rms height, inter-island separation and a combined roughness parameter related to the pressure experienced by each nanowire. It was concluded that the rms height of asperity should not be lower than the radius of nanoparticles for effective lubrication. In addition, when the inter-island separation is an integer multiple of the nanowire length, nanowires perform as effective lubricants. Furthermore, the friction coefficient increased when the mean pressure experienced by the nanowires increased. The results obtained in this original study offer some interesting insights into the frictional properties of NBLS as a function of surface roughness parameters. This could lead to a great impact on the selection of nanoparticle-based lubricant aimed at reducing wear and energy losses for various applications.

Commentary by Dr. Valentin Fuster

Other (Seals, Manufacturing)

J. Tribol. 2012;134(2):022201-022201-7. doi:10.1115/1.4006359.

The effects of gas-rarefaction on dynamic characteristics of micro spiral-grooved-thrust-bearing are studied. The Reynolds equation is modified by the first order slip model, and the corresponding perturbation equations are then obtained on the basis of the linear small perturbation method. In the converted spiral-curve-coordinates system, the finite-volume-method (FVM) is employed to discrete the surface domain of micro bearing. The results show, compared with the continuum-flow model, that under the slip-flow regime, the decrease in the pressure and stiffness become obvious with the increasing of the compressibility number. Moreover, with the decrease of the relative gas-film-thickness, the deviations of dynamic coefficients between slip-flow-model and continuum-flow-model are increasing.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(2):022202-022202-9. doi:10.1115/1.4006407.

This paper presents a new computational fluid dynamics (CFD)/bulk-flow hybrid method to determine the rotordynamic characteristics of annular gas seals. The method utilizes CFD analysis to evaluate the unperturbed base state flow, an averaging method to determine the base state bulk-flow variables, and a bulk-flow perturbation method to solve for the fluid forces acting on an eccentric, whirling rotor. In this study the hybrid method is applied to a hole-pattern seal geometry and compared with experimental data and numerical and analytical methods. The results of this study show that the dynamic coefficients predicted by the hybrid method agree well with the experimental data, producing results that are comparable with a full, three-dimensional, transient, whirling rotor CFD method. Additionally, the leakage rate predicted by the hybrid method is more agreeable with experiment than the other methods. The benefit of the present method is the ability to calculate accurate rotordynamic characteristics of annular seals that are comparable to results produced by full, transient CFD analyses with a simulation time on the order of bulk-flow analyses.

Commentary by Dr. Valentin Fuster

Technical Briefs

J. Tribol. 2012;134(2):024501-024501-5. doi:10.1115/1.4005346.

Choosing the proper metal forming lubricant for nonferrous metals such as aluminum, copper, and brass has become a difficult and complicated decision. The effects of deformation velocity and the influence of deforming material were determined in the two sets of experiments carried out using a single punch with a roughness magnitude Ra of 0.17 μm and four lubricants such as grease, corn oil, VG100, and VG32. In the first set, two different deformation speeds of 0.1 and 1 mm/s were used for cylindrical specimens made of aluminum alloys of 6061-O, 1050-O, and copper alloys tests using a counterpunch die of roughness magnitude Ra of 0.08 μm. In the second set of experiments, cylindrical specimens made of aluminum alloys of AA2024-O and AA6061-O and three deformation speeds of 0.1, 1, and 5 mm/s were used to evaluate the performance of each lubricant under increasing ram speed, but with a roughness magnitude Ra of 0.63 μm. All the lubricants show reduction in maximum load with increasing deformation speed except grease which shows a rise in the maximum load from zero to a maximum at a deformation speed of 1 mm/s and then descends gradually to a minimum load at a speed of 5 mm/s for AA2024-O and AA6061-O. This load reduction seen with grease as lubricant is probably due to thermal softening; therefore grease will not be considered a desirable lubricant under increasing deformation speed because of the adverse effects on the tooling. The present findings show that tip test can be utilized to select an appropriate lubricant for a particular alloy. It reveals that none of the tested lubricants can be used for copper alloy as all the lubricants show increasing measured load for increasing speed magnitude. However, of the liquid lubricants (corn oil, VG100, and VG32) considered, corn oil shows as the best lubricant for cold forging operations of aluminum 6061-O, 1050-O, and 2024-0 under increasing speed magnitude. Also, the tip test has been able to differentiate among materials.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(2):024502-024502-8. doi:10.1115/1.4006443.

A mathematical model of gaseous slip flow in ultra-thin film gas bearings is numerically analyzed incorporating effects of surface roughness, which is characterized by fractal geometry. The Weierstrass-Mandelbrot (W-M) function is presented to represent the multiscale self-affine roughness of the surface. A modified Reynolds equation incorporating velocity slip boundary condition is applied for the arbitrary range of Knudsen numbers in the slip and transition regimes. The effects of bearing number, Knudsen number, geometry parameters of the bearing and roughness parameters on the complex flow behaviors of the gas bearing are investigated and discussed. Numerical solutions are obtained for various bearing configurations under the coupled effects of rarefaction and roughness. The results indicate that roughness has a more significant effect on higher Knudsen number (rarefaction effect) flows with higher relative roughness. Surface with larger fractal dimensions yield more frequency variations in the surface profile, which result in an obviously larger incremental pressure loss. The Poiseuille number increases not only with increasing of rarefaction effect but also with increasing the surface roughness. It can also be observed that the current study is in good agreement with solutions obtained from the linearized Boltzmann equation.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(2):024503-024503-5. doi:10.1115/1.4006022.

The author gratefully acknowledge financial support from the National Institute of Science and Technology (NIST) Advance Technology Program (ATP) Grant No. 70NANB7H7007, and Dr. Jean-Louis Staudenmann, ATP program manager.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(2):024504-024504-4. doi:10.1115/1.4006360.

When a discretized Reynolds equation is to be solved iteratively at least three subjects have to be determined first. These are the iterative solution method, the size of gridwork for the numerical model, and the stopping criterion for the iterative computing. The truncation error analysis of the Reynolds equation is used to provide the stopping criterion, as well as to estimate an adequate grid size based on a required relative precision or grid convergence index. In the simulated lubrication analyses, the convergent rate of the solution is further improved by combining a simple multilevel computing, the modified Chebyshev acceleration, and multithreaded computing. The best case is obtained by using the parallel three-level red-black successive-over-relaxation (SOR) with Chebyshev acceleration. The speedups of the best case relative to the case using sequential SOR with optimal relaxation factor are around 210 and 135, respectively, for the slider and journal bearing simulations.

Commentary by Dr. Valentin Fuster

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