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IN THIS ISSUE


RESEARCH PAPERS

J. Tribol. 1999;121(3):425-432. doi:10.1115/1.2834085.

This paper presents a simple method that may be used to calculate the pressures and surface displacements in contacts of rough surfaces. A main feature of the method is that the pressure is calculated (updated) individually at each surface location rather than simultaneously at all locations by solving a system of equations. The pressure update at a given location is computed solely based on the surface interpenetration at that location; consequently, both 2-D and 3-D contact problems are solved in exactly the same way. Furthermore, this scheme of calculation does not produce negative pressures in the solution process, which is a main source of numerical instability in other types of methods of solution. The method is conceptually simple and easy for computer implementation. It is numerically stable and can solve various types of problems of high contact severity. Measured roughness data can be used directly without any mathematical treatment such as filtering or frequency decomposition. The method is also computationally efficient and requires minimum computer storage, making it suitable for integration into computer programs for design-analysis calculations of practical contact/lubrication problems.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):433-440. doi:10.1115/1.2834086.

Flattening of random rough surfaces on a workpiece undergoing bulk deformation has beenanalyzed using a model of the surface consisting of just two wavelength components. Asperities are flattened at a rate which depends on the ratio of the initial r.m.s. amplitudes of the long and short wavelength components. The flattening behavior of the long wavelength asperities only becomes important when the amplitude of the long wavelength asperitiesis much greater than that of the shorter wavelength asperities. The surface modification was investigated experimentally by cold rolling of aluminium strips. The power spectral density of the roughness was used to extract appropriate amplitudes for the short and longwavelength components of roughness. The change in roughness amplitudes showed excellent agreement with theory.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):441-448. doi:10.1115/1.2834087.

Experimental results are presented along the lines of the early work of Moore (1948) where a hard smooth roller is pressed into a softer rough surface to study the resulting real to apparent areas of contact and their associated local contact pressures. Results are presented for a hard steel roller deforming mild-steel and aluminum-alloy rough surface specimens. An analysis of the local contact mechanics is performed before and after indentation using a recently developed numerical elastic contact simulation method which allows local asperity contact pressures and areas to be studied in detail. The method is shown to reveal the level and distribution of pressures and asperity contact areas prevalent during the indentation process, and therefore allows the contribution of elastic and plastic load support to be quantified. The persistence of asperities during such indentation tests is discussed in terms of the pressures the asperities can support in relation to reported mechanisms of persistence. Results of subsequent sub-surface stresses are also presented and discussed in terms of how the method might be used to create an elastic-plasticdeformation model that can account for asperity persistence in future numerical contact simulation models.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):449-454. doi:10.1115/1.2834088.

The influence of surface roughness on the bulk deformation of line contacts is studied. The model of Greenwood and Tripp (1967) will be extended to line contacts. It is found that the central pressure is a very good parameter to characterize the pressure distribution of rough line contacts. Function fits of the central pressure, the effective half width, the real area of contact, and the number of contacts are made. Comparison is made with the work of Lo (1969) and Greenwood et al. (1984).

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):455-461. doi:10.1115/1.2834089.

Two isotropic linear elastic half-spaces of different material properties are pressed together by a uniform pressure and subjected to a constant shearing stress, both of which are applied far away from the interface. The shear stress is arbitrarily less than is required to produce slipping according to Coulomb’s friction law. Nonetheless, it is found here that the two bodies can slide with respect to each other due to the presence off a separation wave pulse in which all of the interface sticks, except for the finite-width separation-pulse region. In this type of pulse, the separation zone has a vanishing slope at its leading edge and an infinite slope at its trailing edge. Nonetheless, the order of the singularity at the trailing edge is small enough so as not to produce an energy sink. The problem is reduced to the solution of a pair of singular integral equations of the second kind which are solved numerically using a variation of the well-known method of Erdogan et al. (1973). Results are given for various material combinations and for a range of the remote shear-to-normal-stress ratio.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):462-467. doi:10.1115/1.2834090.

The material behavior of the standard bearing steel SAE 52100 and the heat resistant bearing steels M50, M50 NiL, and Cronidur 30 as a function of the operational temperature has been investigated. The reduction in rolling contact fatigue strength due to a temperature rise was found to be significantly higher than the reduction of hardness. The mechanism of heat generation due to the bearing operation induces a temperature distribution, which makes it necessary to distinguish between the temperature ruling the subsurface fatigue processes and a higher temperature dominating the surface originated damage initiation.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):468-472. doi:10.1115/1.2834091.

We have developed a new method for measuring time intervals of Acoustic Emission (AE) generation for diagnosis of a radial rolling bearing. The method makes the AE signal itself a trigger of the oscillation of the clock pulse and measures the time interval of AE generation by integration of the clock pulses. The measurement device consists of the threshold, clock, time interval measurement and memory circuit, and was applied to rolling contact fatigue experiments. It was confirmed by the experiments that the measured time intervals of AE generation on the inner raceway or the ball agreed with the value calculated based on the kinetics of the rolling bearing. Moreover, we could identify the elements in which a fatigue crack was propagating by the method before the spalling appeared. The identified elements agreed with the failed elements.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):473-480. doi:10.1115/1.2834092.

An analytical model is developed in this paper which relates the major component of micro-EHL pressure responses to lubricant properties, roughness geometry, contact load, velocity, and slide-to-roll ratio. Analyses are then conducted showing the effects of system parameters on this micro-EHL pressure. For a Newtonian lubricant with an exponential pressure-viscosity law, this pressure would be large unless the contact practically operates right at pure rolling. The magnitude of the pressure rippling is largely independent of the slide-to-roll ratio, and smaller wavelength components of the surface roughness generate larger micro-EHL pressures. With less dramatic pressure-viscosity enhancement such as the two-slope model, the micro-EHL pressure is generally smaller and sensitive to the slide-to-roll ratio, larger with higher sliding in the contact. Furthermore, this pressure-viscosity model yields a micro-EHL pressure that becomes vanishingly small corresponding to sufficiently small wavelength components of the roughness. For a shear-thinning non-Newtonian lubricant, such as the Eyring model, with an exponential pressure-viscosity law, substantially less micro-EHL pressure rippling is generally developed than its Newtonian counterpart. While the pressure rippling is insensitive of the slide-to-roll ratio like its Newtonian counterpart, it vanishes corresponding to sufficiently small wavelength components of the roughness. The analyses revealed that a key factor resulting in a smaller micro-EHL pressure with the two-slope model or the Eyring model is the lower viscosity or shear-thinned effective viscosity in the loaded region of the contact. Since EHL traction is proportional to this viscosity, contacts lubricated with oils exhibiting higher traction behavior would develop larger micro-EHL pressures and thus would be more vulnerable to fatigue failure.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):481-491. doi:10.1115/1.2834093.

Most machine elements, such as gears and bearings, are operated in the mixed lubrication region. To evaluate lubrication performance for these tribological components, a contact model in mixed elastohydrodynamic lubrication is presented. This model deals with the EHL problem in the very thin film region where the film is not thick enough to separate the asperity contact of rough surface. The macro contact area is then divided into the lubricated area and the micro asperity contact areas by the contacted rough surfaces. In the case when asperity to asperity contact is present, Reynolds equation is only valid in the lubricated areas. Asperity contact pressure is determined by the interaction of two mating surfaces. The applied load is carried out by the lubricant film and the contacted asperities. FFT techniques are utilized to calculate the surface displacement (forward problem) by convolution and the asperity contact pressure (inverse problem) by deconvolution for non-periodic surfaces. With the successful implementation of FFT and multigrid methods, the lubricated contact problem can be solved within hours on a PC for the grids as large as one million nodes. This capability enables us to simulate random rough surfaces in a dense mesh. The load ratio, contact area ratio and average gap are introduced to characterize the performance of mixed lubrication with asperity contacts. Discussions are given regarding the asperity orientation as well as the effect of rolling-sliding condition. Numerical results of real rough topography are illustrated with effects of velocity parameter on load ratio, contact ratio, and average gap.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):492-498. doi:10.1115/1.2834094.

Formulation of a three-dimensional, quasi-static lubrication model of an artificial hip joint is proposed which includes the inclination angle of the acetabular cup. This is performed by deriving a transformed Reynolds equation accounting for this cup tilt angle. The numerical simulation also addresses mass conservation at the location of film rupture. A 3-D spherical representation of the articulating surfaces of the hip prosthesis is mapped onto a cartesian coordinate system of the entire geometry of the “ball and socket” joint. Results include the lubricating fluid pressure distributions for various inclination angles of the acetabular cup demonstrating that the greatest pressures occur for large eccentricities in the upward vertical direction.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):499-505. doi:10.1115/1.2834095.

A complete method is presented to calculate the stiffness and the damping coefficients in a hydrodynamic bearing considering five degrees of freedom for a general rotor-bearing system. Perturbation equations are obtained from Reynolds equation by assuming the small amplitude motion of a bearing center, and are solved by the finite element method. Their characteristics due to eccentricity and misalignment are investigated for herringbone groove journal and thrust bearings in the spindle motor of a hard disk drive. This research shows that the dynamic coefficients increase with increasing the misalignment as well as the eccentricity due to the wedge effect. It also shows that the moment coefficients, which have been neglected in most of the previous analyses, are of significant magnitude in a journal bearing and have even bigger values for the thrust bearing when they are compared with the ball bearing in the same type of a spindle motor.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):506-509. doi:10.1115/1.2834096.

This paper proposes a newly developed laser scanner motor with low power consumption, operating at a high speed of rotation. The principle of the scanner motor is that of a herringbone-grooved journal bearing functioning as a viscous vacuum pump. The windage power loss of a polygon mirror can be reduced because the air inside the housing is pumped out by herringbone-grooved viscous vacuum pumps. The performance of the proposed laser scanner motor was measured under various conditions. It was subsequently found that the proposed scanner motor of a laser beam had much reduced power consumption and higher scanning accuracy than the conventional scanner motor in which the rotor is rotated in the air.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):510-516. doi:10.1115/1.2834097.

We investigated the lubricating characteristics between a vane and piston lubricated with an oil-refrigerant mixture. Theoretical analyses were performed using mixed elastohydrodynamic lubrication analysis theory, taking metallic contacts into account. Lubricating conditions were evaluated by comparing the theoretical results of piston dynamics based on actual surface roughness distributions measured by SEM, with the experimental results measured under practical operation. We conclude that (1) lubricating conditions between the vane and piston can be assumed to be within the mixed lubricating zone, in which the coefficient of friction changes from 0.04 to 0.08, and the contact force is almost equally supported by oil film and metallic contact; (2) the coefficient of friction decreases as the contact force increases because the ratio of pressure rise of the oil film to the decrease in clearance is much greater than that for metallic contact pressure; and (3) in mixed EHL analysis, it is important not only to measure the actual surface roughness but also to select the appropriate contact model.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):517-522. doi:10.1115/1.2834098.

An experimental study is performed to investigate the frequency effects of the excitation force on the linear stiffness and damping coefficients of a LOP (load on pad) type five-pad tilting pad journal bearing with the diameter of 300.91 mm and the length of 149.80 mm. The main parameter of interest in the present work is excitation frequency to shake the test hearing. The excitation frequency is controlled independently, using orthogonally mounted hydraulic exciters, as follows: 1) excitation frequency ratio in the x-axis direction νx = 0.5, 2) excitation frequency ratio in the y-axis direction νy = 0.6, 0.7, 0.8, 0.9. The magnitude of the excitation force is controlled to make sure that the test hearing has a linear behavior during the test. The relative movement between the bearing and shaft, and the acceleration of the bearing casing are measured as a function of excitation frequency using the different values of bearing load and shaft speed. Measurements show that the variation of excitation, frequency has quite a little effect on both stiffness and damping coefficients. The stiffness coefficients of the five-pad tilting pad journal bearing slightly decrease as the excitation frequency ratio increases, while the damping coefficients slightly increase with excitation frequency ratio, especially in the case of lower speed and higher load. Both direct stiffness and damping coefficients in the direction of bearing load decrease with an increase of shaft speed, but increase with the bearing load.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):523-528. doi:10.1115/1.2834099.

A finite element fluid-structure coupling is developed in order to simulate a lubricated forming process, A dynamic explicit code is used for elasto-plastic deformation calculations and normal and tangential contact conditions are handled using a dynamic projection method. Two complementary approaches to the hydrodynamic lubrication problem are proposed: a classical method using the direct solution of the inverse hydrodynamic problem and an original indirect method based on the so called “optimal control theory.” The applicability of the code developed is proved by the numerical simulation of an industrial ironing process. Results of the two methods are compared in terms of friction forces and film thickness profiles. The distribution of local friction coefficients is also obtained.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):529-537. doi:10.1115/1.2834100.

Successive steps in constructing a realistic conservative 3D model for hydrodynamic porous bearings are presented. They consist in iterative comparisons between theoretical results and industrial knowledge. This model is based on Darcy’s law for the porous bearing and an adaptation of Elrod’s model to a generalized Reynolds’s equation for the flow in the gap between the shaft and the bearing. Capillary effects at the outer surface of the bearing, and pore obstruction at its inner surface, leading to loss of permeability in the region where film thickness is minimal, are highlighted as phenomena which can prevent bearing leakage. They have been taken into account in the boundary conditions of the proposed model.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):538-545. doi:10.1115/1.2834101.

Hydrodynamic fluid lubrication theory is applied to thrust bearings with three-dimensional, wave-shaped axial end surfaces. Optimizations of the wave height and surface porosity are experimentally determined using lubrication characteristics such as the friction coefficient and worn-out surface conditions. Lubrication characteristics such as the friction coefficient, temperature rise, thrust flotation, and oil consumption rate are evaluated for an estimation of life expectancy. In this research, the results of this theoretical application on thrust bearings clearly showed considerable improvement over conventional thrust bearings. Furthermore, this experimental research has clarified the lubrication conditions of various thrust-loaded axial end surfaces.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):546-552. doi:10.1115/1.2834102.

An isothermal journal bearing that incorporates heat-pipe cooling technology has been developed. The heat pipe can spread frictional heat rapidly along the bearing circumference, resulting in a uniform temperature distribution in the bearing with a low peak temperature and stable transient thermal performance. A numerical model has been developed for the new bearing to facilitate a thorough understanding of its performance as well as an optimal bearing design. The heat pipe in the bearing is modeled as a heat conductor whose effective thermal conductance is determined through the correlation between the numerical results and experimental data. The heat transfer coefficients at bearing boundaries are obtained with the assistance of experimental measurements and calculations using semi-empirical correlations. Good agreement is observed between the analytical and experimental results. Once the analytical model is validated, a parametric study is conducted for the performance of new bearings with different configurations and materials. The analytical results further confirm that the isothermal journal bearing developed has the ability to battle frictional-heat-induced problems, which can significantly benefit both bearing operation and failure prevention.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):553-559. doi:10.1115/1.2834103.

The increasing effort to use sub-ambient pressure air bearing sliders for dynamic load/unload applications in magnetic hard disk drives requires desirable air bearing characteristics during the dynamic unload event. This paper establishes air bearing design criteria for achieving a smooth head unload performance, through a correlation study between the modeled unloading air bearing dynamics of two 30 percent proximity recording sub-ambient pressure sliders and motion sequence of the same sliders by a high-speed video camera. It is shown that the air bearing lifting force quickly responds to changes in fly height and pitch, while the suction force is relatively resistant to changes in fly height, but somewhat more sensitive to changes in pitch. This unique distinction results in different decreasing rates between the air bearing lifting and suction forces during the unload process, creating a strong dependence of the unloading characteristics on the location of the suction cavities. Both the modeled unloading air bearing dynamics and experimentally recorded motion sequence illustrate that a toward-trailing-edge located suction force acts to pitch the slider up, while the moment produced by a toward-leading-edge located suction force induces a negative pitch motion, resulting in an excessive flexure deformation and dimple separation. Therefore, placing the suction cavities towards the trailing edge offers a reliable unloading performance for the sub-ambient pressure air bearing sliders.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):560-567. doi:10.1115/1.2834104.

The revival of dynamic load/unload (L/UL) technology forces us to rethink the air bearing design philosophy, which has traditionally been established for contact start/stop applications. Reliably loading a slider onto a full-rotating disk imposes its own requirements on the slider air bearing designs. This paper addresses the unique design requirements of dynamic L/UL technology, through an investigation of the air bearing characteristics of two proximity recording sliders during a dynamic load process. While the slider/disk contact force is employed as a key indicator of the reliability of the dynamic load mechanism, the air bearing suction force and squeeze flow effect are used to characterize the slider’s dynamics during loading. The effects of the slider’s loading velocity, pitch and roll static attitudes on its dynamic load performance are simulated. In comparison to the positive pressure air bearings, both the enlarged air bearing surface and shallowly recessed cavities of the subambient pressure air bearing sliders generate more squeeze flow, resulting in a rapid development of the air bearing lifting force at a higher attitude. This often leads to a more reliable dynamic load performance. The impact of the air bearing suction force on the slider’s dynamics during loading is determined by the suction force center. A towards-leading-edge suction force not only induces a negative pitch motion during the early stage, but also prolongs the pitch-up process. Both effects can result in a head crash for the slider with a large negative pitch static attitude. In summary, the subambient pressure air bearing sliders that feature the enlarged leading air bearing surface and towards-trailing-edge suction cavities with small recess depth offer a fast pitch-up load performance.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):568-574. doi:10.1115/1.2834105.

Air bearing slider dynamic performance during the ramp loading and unloading processes was investigated theoretically in this paper. The air bearing was modeled by the modifiedcompressible Reynolds equation, and it was solved by the finite volume method. Slider dynamic equations were derived in this paper to include the ramp loading/unloading mechanism. These two sets of coupled equations were solved iteratively. Both Tripad and negative pressure air bearing (NPAB) were included in the analysis. Effects of loading/unloading velocity, disk rotational speed, as well as suspension flexure stiffness, were investigated. Slider-disk impact will occur during the Tripad loading process, especially at high loading velocity. On the other hand, this impact can be avoided for an NPAB at loading velocity up to 200 mm/s. However, an NPAB requires a longer unloading time due to its suction force. This unloading process is further delayed if a soft flexure is combined with an NPAB.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):575-580. doi:10.1115/1.2834106.

This study proposes a design methodology for determining configurations of subamient pressure shaped rail sliders by using a nonlinear programming technique in order to meet the desired flying characteristics over the entire recording band. The desired flying characteristics considered in this study are to minimize the variation in flying height from a target value, to keep the pitch angle within a suitable range, and to ensure that the outside rail flies lower than the inside rail even with the roll distribution due to manufacturing process. The design variables selected are recess depth, geometry of the air bearing surface, and pivot location in the transverse direction of the slider. The method of feasible directions in Automated Design Synthesis (ADS) is utilized to automatically find the optimum design variables which simultaneously meet all the desired flying characteristics. To validate the suggested design methodology, a computer program is developed and applied to a 30 percent/15 nm twin rail slider and a 30 percent/15 nm tri-rail slider. Simulation results for both sliders demonstrated the effectiveness of the proposed design methodology by showing that the flying characteristics of the optimally designed sliders are enhanced in comparison with those of the initial ones.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):581-586. doi:10.1115/1.2834107.

The “take-off” behavior of proximity recording sliders is investigated using acoustic emission and phase demodulated laser interferometry. A biquadratic surface fit of the air bearing surface is used to determine the position of the slider with respect to the disk. Acoustic emission data is examined in both the time and frequency domain to analyze the location of slider/disk contacts. Two distinct frequencies are observed in the frequency spectrum of the acoustic emission signal, corresponding to torsional mode and bending mode vibrations of the rigid slider. As the velocity increases, the magnitude of the torsional mode decreases relative to that of the bending mode, indicating that slider/disk contacts change from side rails contacts to trailing edge contacts.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):587-595. doi:10.1115/1.2834108.

This study is a computational analysis of the bouncing vibration of a point contact slider model over computer generated random disk surfaces and the design conditions of slider to disk interface parameters necessary for contact recording. The Gaussian random surface of a disk with various standard deviations and frequency characteristics is generated by using a modified midpoint displacement algorithm. From the calculated results of bouncing vibration of a slider for various parameter values, it was found that the decrease in contact stiffness and increase in slider load can significantly reduce the bouncing vibration as well as the increase in contact damping and the smoothness of the surface. It was also found that the bouncing vibration spectrum of a contact slider over a simulated disk surface agreed closely with the experimental results presented in a previous study by the authors. The maximum and rms values of the spacing and the contact force were examined for various design parameters. The design conditions of the contact pad to the disk interface were discussed in terms of tracking ability and wear durability for slider loads of 0.5 mN and 5 mN.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):596-603. doi:10.1115/1.2834109.

The general characteristics of the bouncing vibrations of a IDOF contact slider model over the surface of a harmonic wavy disk were studied both by computer simulation and theoretical analysis. The necessary design conditions for a contact slider and the surface of a disk were discussed in terms of perfect contact sliding and wear durability. It was found that the bouncing vibrations change with the amount of waviness amplitude A(fr ) at the contact resonant frequency fr (= (1/2π)kc/m) relative to static penetration depth δ, or fr relative to limiting critical frequency fcl , above which the downward acceleration of the surface of a disk is larger than that of a slider due to slider load. When the contact stiffness is large enough so that δ < A(fr ) (fcl < fr ), the slider bounces with a large amplitude similar to an elastic impact in a wide frequency range. When the contact stiffness is small enough so that δ > A(fr ) (fcl > fr ), bouncing vibrations occur near the contact resonance, similar to the resonance of a nonlinear soft spring system. Here, the bouncing vibration can be completely eliminatedby increasing the contact damping ratio and decreasing the slider mass and the waviness amplitude.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):604-609. doi:10.1115/1.2834110.

A journal bearing simulation tool developed to aid the design of the MIT microturbo-machine bearings is described. This tool uses an orbit method with a pseudospectral technique for treating the Reynolds equation. Comparison is made to various published data. Two types of stability chart are presented and their application to turbo-machine bearing design is discussed. Simulations of imbalance, noncircular geometry, and nonuniform pressures at the bearing ends are also demonstrated.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):610-617. doi:10.1115/1.2834111.

A comprehensive formulation of the governing equations, boundary conditions, and numerical solution technique is presented for modeling the thermal aspects of the engagement process in a wet clutch. The thermal model includes full consideration of the viscous heat dissipation in the fluid as well as heat transfer into the separator, friction material, and the core disk. Roughness, waviness, deformability and permeability of the friction material are taken into account. It is shown that very large temperatures develop in the fluid during the engagement process which takes place on the time scale of one second. It is also shown that thermal effects influence the engagement time and the torque behavior of a clutch and should be included in the analytical studies.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):618-624. doi:10.1115/1.2834112.

A simple algorithm has been developed for predicting traction in web handling applications. Minimal traction exists when the minimum air film height between the roller and web is greater than three times the rms roughness of the two surfaces in contact. Classical foil bearing theory modified for permeable surfaces is used to determine the air film height. A piecewise linear solution using squeeze film theory is also used to account for side leakage. The minimum air film height is a function of web tension, web and roller velocity, air viscosity, web width, web permeability and roller radius. The algorithm is applicable for permeable and nonpermeable webs. Values obtained from the algorithm can be used to predict if sufficient traction is available between the web and roller for a given set of physical and operating parameters. Traction values can also be used as input for winding, wrinkling, and spreading models.

Commentary by Dr. Valentin Fuster
J. Tribol. 1999;121(3):625-630. doi:10.1115/1.2834113.

As part of a program to develop solid/powder-lubricated journal bearings, a comparative evaluation has been performed to aid in determining whether MoS2 and WS2 powder are suitable lubricants for high-speed, extreme-environment multi-pad journal bearings. Plots of traction coefficients, friction, frictional power loss, and bearing pad temperature are presented as a means for comparing various powder lubricants. This paper primarily focuses on experiments carried out on a three-pad journal bearing and a disk-on-disk tribometer. Results showed that MoS2 traction curves resemble that of SAE 10 synthetic oil. Unlike liquid lubricants, powder films have a limiting shear strength property. Once the powder reaches this limiting value, the maximum traction coefficient is limited and the powder essentially shears along sliding walls. Experimental traction data shows evidence of this property in various powders. The thermal performance of the bearing was evaluated at speeds up to 30,000 rpm and loads up to 236 N. Although WS2 displayed constant friction coefficient and low temperature with increasing dimensionless load, MoS2 exhibited frictional behavior resembling that of a hydrodynamic lubricating film. In this paper, an attempt has been made to provide a criterion for the selection of solid lubricants for use in those tribosystems that may be operated in a high speed/load regime (i.e., high strain rates) as an alternative yard stick to conventional comparative approaches.

Commentary by Dr. Valentin Fuster

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