Transient behavior of tribo-characteristics caused by micro-dimples on point contact surfaces with different mechanical and thermal properties was investigated based on non-Newtonian thermal EHL analysis. The dimples were assumed to exist on both contact surfaces and the surface shapes of the contact bodies were evaluated separately. It is pointed out that surface texturing due to the micro-dimples is not necessarily beneficial in EHL contacts under fully flooded conditions, since the micro-dimples provide a high pressure and a thin minimum film thickness as compared to the case of contacts with smooth surfaces, although the friction coefficient of surfaces with micro-dimples is always lower than that of the smooth surfaces. In order to obtain relatively good tribo-characteristics, the velocity of the surface with low thermal conductivity should be faster than that with high thermal conductivity, and the wavelengths of micro-dimples in the direction of motion on both surfaces should be different.

Pastewka and Robbins (2014, “Contact Between Rough Surfaces and a Criterion for Macroscopic Adhesion,” Proc. Natl. Acad. Sci., 111 (9), pp. 3298–3303) recently have proposed a criterion to distinguish when two surfaces will stick together or not and suggested that it shows quantitative and qualitative large conflicts with asperity theories. However, a comparison with asperity theories is not really attempted, except in pull-off data which show finite pull-off values in cases where both their own criterion and an asperity based one seem to suggest nonstickiness, and the results are in these respects inconclusive. Here, we find that their criterion corresponds very closely to an asperity model one (provided we use their very simplified form of the Derjaguin–Muller–Toporov (DMT) adhesion regime which introduces a dependence on the range of attractive forces) when bandwidth α is small, but otherwise involves a root-mean-square (RMS) amplitude of roughness reduced by a factor α . Therefore, it implies that the stickiness of any rough surface is the same as that of the surface where practically all the wavelength components of roughness are removed except the very fine ones.

This work presents a finite element (FE) study of a perfectly elastic axisymmetric sinusoidal-shaped asperity in contact with a rigid flat for different amplitude to wavelength ratios and a wide range of material properties. This includes characterizing the pressure required to cause complete contact between the surfaces. Complete contact is defined as when there is no gap remaining between two contacting surfaces. The model is designed in such a way that its axisymmetric and interaction with the adjacent asperities are considered by the effect of geometry at the base of the asperity. The numerical results are compared to the model of curved point contact for the perfectly elastic case (known as Hertz contact) and Westergaard's solution. Once properly normalized, the nondimensional contact area does not vary with nondimensional load. The critical pressure required to cause complete contact is found. The results are also curve fitted to provide an expression for the contact area as a function of load over a wide range of cases for use in practical applications, such as to predict contact resistance. This could be a stepping stone to more complex models.

In the current study, a semi-analytical model for contact between a homogeneous, isotropic, linear elastic half-space with a geometrically anisotropic (wavelengths are different in the two principal directions) bisinusoidal surface on the boundary and a rigid base is developed. Two asymptotic loads to area relations for early and almost complete contact are derived. The Hertz elliptic contact theory is applied to approximate the load to area relation in the early contact. The noncontact regions occur in the almost complete contact are treated as mode-I cracks. Since those cracks are in compression, an approximate relation between the load and noncontact area can be obtained by setting the corresponding stress intensity factor (SIF) to zero. These two asymptotic solutions are validated by two different numerical models, namely, the fast Fourier transform (FFT) model and the finite element (FE) model. A piecewise equation is fit to the numerical solutions to bridge these two asymptotic solutions.

The effect of single-sided and double-sided harmonic surface waviness on the film thickness, pressure, and temperature oscillations in an elastohydrodynamically lubricated eccentric-tappet pair has been investigated in relation to the eccentricity and the waviness wavelength. The results show that, during one working cycle, the waviness causes significant fluctuations of the oil film, pressure, and temperature, as well as a reduction in minimum film thickness. Smaller wavelength causes more dramatic variations in oil film. The fluctuations of the pressure, film thickness, temperature, and traction coefficient caused by double-sided waviness are nearly the same compared with the single-sided waviness, but the variations are less intense.

Many elastohydrodynamically lubricated contacts in practical applications, e.g., in bearings, operate in the starved lubrication regime. As a result their performance is sensitive to variations of the lubricant layers present on the surfaces, which form the supply to the contact. Their shape is often determined by previous overrollings of the track and also by replenishment mechanisms and various migration effects. Variations of the layers induced in the direction of rolling lead to a time-varying lubricant supply to the contact. In this paper, by means of numerical simulations using a starved lubrication model, the film thickness modulations in the center of the contact induced by a harmonically varying inlet supply have been investigated. First, for a given load condition and layer wavelength, the effect of the nominal layer thickness (degree of starvation) and the layer variation amplitude is illustrated. Subsequently, using results for different load conditions, wavelengths, and degrees of starvation, it is shown that the response of the contact to such variations is determined by a nondimensional parameter, which represents the ratio of the entrainment length of the contact to the wavelength of the induced variation, and by the degree of starvation. A simple formula is presented for use in engineering predicting the ratio of the amplitude of the film modulations in the center of the contact to the amplitude of the layer variations in the inlet.

The influence of the transversely and/or longitudinally oriented surface waviness on the lubricating behavior in the rolling/sliding elliptic contact composed of two steel bodies and lubricated with a non-Newtonian lubricant was investigated theoretically with full numerical solution of the thermal elastohydrodynamic lubrication. The entrainment velocity was assumed to be along the minor axis of the Hertzian contact ellipse. The waviness of each surface was given by a sinusoidal function. The non-Newtonian flow of the lubricant was described by the Eyring model with a constant Eyring shear stress at the ambient pressure and temperature. The velocity of the faster surface was assumed to be four times as that of the slower surface in order not only to highlight the thermal and non-Newtonian effects, but also to ensure a cyclic solution when both surfaces were with transversely oriented waviness. Starting from a quasisteady solution, the cyclic time-dependent solution was achieved numerically time step by time step. The results show that the thermal and non-Newtonian effects can be enlarged significantly by the surface waviness, and the worst configuration of the surface topography is that both surfaces are with longitudinal waviness.

Influence of corrugation of limited extent on the performance of fixed-incline slider bearings of infinite width is investigated numerically. Effects of the corrugated section’s parameters like its location, length, and corrugation amplitude, on pressure distribution in the bearing’s fluid film, its load supporting capacity W and flow rate, are considered. When this section is near the entrance to the bearing gap, pressure and W are reduced in comparison with the smooth wall case. As this section is located further downstream, peak pressure and W increase, whereas flow rate decreases. These effects are reinforced by longer corrugated section and larger corrugation amplitude. The results thus point to a simple way to substantially enhance a bearing’s load-supporting capacity.

We demonstrated the direct visualization of molecularly thin lubricant films on magnetic disks with a thickness resolution of 0.1 nm by using an ellipsometric microscope with a white light source. It was able to reduce the optical interference noise that arises in conventional laser-based ellipsometric microscopes and to provide a larger SNR by a factor of about 6 compared to a laser-based ellipsometric microscope. The wavelength width should be given first priority in designing a white-light-source ellipsometric microscope, and the width should be determined after considering the required coherence length and thickness resolution. Theoretical calculations indicate that a wavelength width of less than 10 nm can provide a thickness resolution of 0.1 nm. A white-light-source ellipsometric microscope can provide real-time visualization of a molecularly thin lubricant film with a thickness resolution of 0.1 nm, which is useful in investigating the kinetic behavior of molecularly thin lubricant films on magnetic disks.

The objective of this paper is to investigate the flow in a lubricant film on the surface roughness scale and to compare the numerical solutions obtained by two different solution approaches. This is accomplished firstly by the CFD-approach (computational fluid dynamic approach) where the momentum and continuity equations are solved separately, and secondly the Reynolds equation approach, which is a combination and a simplification of the above equations. The rheology is assumed to be both Newtonian and non-Newtonian. An Eyring model is used in the non-Newtonian case. The result shows that discrepancies between the two approaches may occur, primarily due to a singularity which appears in the momentum equations when the stresses in the lubricant attain magnitudes that are common in EHL. This singularity is not represented by the Reynolds equation. If, however, the rheology is shifted to a non-Newtonian Eyring model the deviations between the two solution approaches is removed or reduced. The second source of discrepancies between the two approaches is the film thickness to wavelength scale ω. It will be shown that the Reynolds equation is valid until this ratio is approximately O 10 − 2 .

This paper presents a numerical study comparing the performance of air bearing slider form-factors. The air bearing slider and air bearing surface (ABS) design has gone through drastic changes in recent years in order to achieve the performance required by lower flying heights. In the past, improvements have been seen by scaling down the form-factors of air bearing sliders. The pico form-factor 1.25 × 1 mm has been successfully used for several generations of products and the question arises—should the form-factor be scaled down further? The dynamic characteristics and flying-height modulation (FHM) performance of two different ABS designs in the pico and femto 0.82 × 0.66 mm form-factors were numerically investigated. It was found that for the smaller form-factor designs, greater damping of the air bearing film and slider body system was achieved but with an undesirable decrease in modal frequencies. However, depending on the ABS design, beneficial dynamic properties can be achieved by scaling down the form-factor from pico to femto. Maximizing the total air bearing force (the sum of negative and positive) with a design featuring a large number of transverse pressure gradients can obtain high stiffness and damping. Geometric FHM was also investigated using both sinusoidal disk waviness and an actual measured disk topography. It was found that the FHM depends not only on the form-factor, but also on the ABS design. For long disk waviness wavelengths (longer than the slider body length, L ), the FHM is proportional to L β where β was found to be between 2.6 and 4; hence, FHM is dependent on form-factor. For short disk waviness wavelengths, the FHM is a function of the ABS design and flying attitude and not form-factor. A disk waviness wavelength of 3 mm demarks the transition above which the FHM is a function of form-factor and below which the FHM is a function of the ABS design and the superposition of these two effects compose the geometric FHM. Simulations with an actual measured disk topography showed that the femto form-factor exhibited 22–32 percent less FHM than the pico form-factor for a similar design. However, by changing the ABS design, 35–40 percent less FHM was achieved within the same form-factor. By scaling down a pico slider to a femto slider, we do not necessarily achieve enhanced overall performance. Significant performance improvements in the pico form-factor can be attained if the ABS is properly designed. However, in designing a dynamically stable and low FHM air bearing slider a femto slider ultimately yields better performance when care is taken in designing the ABS.

The effect of longitudinal roughness on the friction in EHL contacts is investigated by means of numerical simulations. In the theoretical model the Eyring equation is used to describe the rheological behavior of the lubricant. First the relative friction variation caused by a single harmonic roughness component is computed as a function of the amplitude and wavelength for a wide range of operating conditions. From the results a curve fit formula is derived for the relative friction variation as a function of the out-of-contact geometry of the waviness and a newly derived parameter characterizing the response of the lubricant to pressure variations. Subsequently, the case of a superposition of two harmonic components is considered. It is shown that for the effect on friction such a combined pattern can be represented by a single equivalent wave. The amplitude and the wavelength of the equivalent wave can be determined from a nonlinear relation in terms of the amplitudes and wavelengths of the individual harmonic components. Finally the approach is applied to the prediction of the effect of a real roughness profile (many components) on the friction. From a comparison of the results with full numerical simulations it appears that the simplified approach is quite accurate.

By means of numerical simulations the deformation of transverse and isotropic harmonic waviness in EHL circular contacts under pure rolling has been studied in relation to the lubricant supply to the contact. In earlier work the deformation of waviness under pure rolling in a fully flooded contact was shown to depend on a single non-dimensional wavelength parameter. In terms of this parameter short wavelengths deform very little. In this paper the effect of starvation on this behavior is shown. First, the steady state smooth surface problem is discussed as an introduction and as a reference problem. It is illustrated in detail how the entire film thickness level decreases with decreasing lubricant supply. Subsequently, results are presented for the time dependent problem with waviness moving through the contact under pure rolling. The relative deformed amplitude of the waviness inside the contact is shown to depend on the same non-dimensional wavelength parameter as before, but also on the degree of starvation. A smaller lubricant supply leads to a larger reduction of the waviness amplitude inside the contact. Finally, it is shown that to an acceptable accuracy the relative deformed amplitude of the starved problem can be predicted by the formula for the fully flooded problem if the generalized wavelength parameter is modified using the reduction factor of the central film thickness for the starved steady state smooth contact. For this reduction factor an accurate formula is available and as a result also for starved contacts by means of a component wise approach a crude estimate of the deformed surface micro-geometry (roughness) inside a contact can be obtained quite easily now.

A two-dimensional friction model has been developed for cold metal rolling in the “mixed” lubrication regime. Roughness is modelled using superimposed short and long wavelength asperities with a lay orientated along the rolling direction. The hydrodynamic pressure in the lubricant is solved using Reynolds’ equation, coupled with the crushing process of the two-wavelength roughness. This allows for the solution of film thickness and contact area ratio and hence friction coefficient through the roll-bite. The model extends the authors’ earlier model [15] by allowing for a variation in hydrodynamic pressure across the width of the contact. Predictions for both the surface roughness and the friction coefficient are in reasonable agreement with published measurements.

Present understanding of the mechanisms of lubrication and the load carrying capacity of lubricant films mainly relies on models in which the Reynolds equation is used to describe the flow. The narrow gap assumption is a key element in its derivation from the Navier Stokes equations. However, the tendency in applications is that lubricated contacts have to operate at smaller film thickness levels, and because engineering surfaces are never perfectly smooth, locally in the film this narrow gap assumption may violated. In addition to this geometric limitation of the validity of the Reynolds equation may come a piezoviscous and compressibility related limitation. In this paper the accuracy of the predictions of the Reynolds model in relation to the local geometry of the gap is investigated. A numerical solution algorithm for the flow in a narrow gap has been developed based on the Stokes equations. For a model problem the differences between the pressure and velocity fields according to the Stokes model and the Reynolds equation have been investigated. The configuration entails a lower flat surface together with an upper surface (flat or parabolic) in which a local defect (single asperity) of known geometry has been embedded. It is investigated how the magnitude of the differences develops as a function of the geometric parameters of the film and the feature. Finally, it is discussed to what extend for these problems a perturbation approach can provide accurate corrections to be applied to the Reynolds solution.

Two new air bearing slider designs are presented for storage densities greater than 100 Gb/in 2 in hard disk drive (HDD) applications. Their dynamic frequencies and mode shapes are characterized, and they are used to study the flying height modulation (FHM) over wavy disks due to geometric effects as opposed to dynamic effects. It is found that low pitch designs experience large FHM at wavelengths on the order of the length of the sliders to one-eighth the length of the sliders due to a complex phase shift in the sliders trailing edge response as compared to the disk waviness. FHM due to disk waviness wavelengths from 2 mm to 0.16 mm was found to be a function of the sliders’ attitude (pitch angle) and the air bearing surface (ABS) geometry (pressure distribution over the ABS). The results presented suggest that the pitch should be greater than 100 μrad for the ABS designs presented and attention needs to be focused on the ABS design and disk morphology to avoid unacceptable FHM. An ABS design was introduced to reiterate the findings on geometric FHM showing an 83 percent decrease in geometric FHM. The FHM due to geometric effects of the slider designs studied in this paper could possibly be predicted by the disk morphology alone.

It is today possible to manufacture so smooth surfaces that they can elastically conform totally to each other over the whole Hertzian contact area. For pure rolling lubrication such surfaces only need an oil film of molecular dimensions to get total separation. When the rolling motion is combined with sliding, the pressure fluctuations inside the Hertzian contact redistribute the oil and make metal-to-metal contact possible. The redistribution velocity is a function of the slip rate S and the number of asperities N from the inlet to the outlet of the Hertzian contact area. The asperity top oil film thickness decreases with a factor of the order 2 NS going from the inlet to the outlet of the Hertzian contact.

A transient finite element simulation is developed for the two-dimensional thermoelastic contact problem of a stationary layer between two sliding layers, with frictional heat generation. The Petrov-Galerkin algorithm is used to discretize the sliding layers because of the high Peclet numbers involved. The results in the linear, full contact regime were validated by comparison with the analytical predictions of Lee and Barber (1993). After separation occurs, there is a non-monotonic transition to a steady state with the contact regions separated by the same wavelength. During the transition, the migration speed exhibits values lower than those in either the linear regime or the final steady state. When several wavelengths are unstable, the final steady state is generally that corresponding to the longest unstable wavelength, even though other modes have more rapid growth rates in the linear regime.

Finite element analysis is applied to simulate the head/tape interface in a Digital Linear Tape (DLT) drive. The numerical model was verified by contact spacing measurements using a “three-bump” glass head and three-wavelength interferometry. The effect of tape speed, tension and head contour parameters (island width, island radius, and penetration) on the head/tape spacing is investigated numerically for a three-bump and a five-bump DLT-type head. A “Local Tape Wrap Angle” is defined to characterize the head/tape interface.

When a metal is surface ground the roughness generated is the summation of a function of the wheel roughness and the roughness due to wheel attrition and damage to the workpiece. We identify this function here as a maximum envelope profile, which is fractal within certain cut off wavelengths determined by the dressing conditions of the wheel. Estimating the global displacement of the binder-grit-workpiece system from the maximum envelope power spectra, we determine the plastic indentation of the workpiece at characteristic length scales using simple contact-mechanical calculation. The estimated roughness corresponds well with that recorded experimentally for hard steel, copper, titanium and aluminium.