Showing papers in "Journal of Tribology-transactions of The Asme in 2004"

A Static Friction Model for Elastic-Plastic Contacting Rough Surfaces

Abstract: A model that predicts the static friction for elastic-plastic contact of rough surfaces is presented. The model incorporates the results of accurate finite element analyses for the elastic-plastic contact, adhesion and sliding inception of a single asperity in a statistical representation of surface roughness. The model shows strong effect of the external force and nominal contact area on the static friction coefficient in contrast to the classical laws of friction. It also shows that the main dimensionless parameters affecting the static friction coefficient are the plasticity index and adhesion parameter The effect of adhesion on the static friction is discussed and found to be negligible at plasticity index values larger than 2. It is shown that the classical laws of friction are a limiting case of the present more general solution and are adequate only for high plasticity index and negligible adhesion. Some potential limitations of the present model are also discussed pointing to possible improvements. A comparison of the present results with those obtained from an approximate CEB friction model shows substantial differences, with the latter severely underestimating the static friction coefficient.

Effect of Deterministic Asperity Geometry on Hydrodynamic Lubrication

Abstract: This paper presents a numerical study of the effects of different shapes of deterministic microasperities in sliding surface lubrication when hydrodynamic films are found. Positive (protruding) and negative (recessed) asperities of constant height (depth) are considered with circular, square, diamond, hexagonal and triangular cross-sections. Of particular interest is the impact of asperity/cavity cross-sectional geometry on friction and leakage, which has importance in sealing applications. The results indicate that the friction coefficient is insensitive to asperity/cavity shape, but quite sensitive to the size of the cross-section. By contrast, leakage rates are found to be quite sensitive to both cross-sectional shape and size, with triangular asperities giving the smallest leakage rate and square asperities giving a largest leakage rate. The minimum coefficient of friction for all shapes is found to occur at an asperity area fraction of 0.2 for positive asperities and 0.7 for negative asperities. Finally, the results indicate the existence of a critical asperity area fraction where the performance curves for positive and negative asperities cross over These cross-over points are identified for friction coefficient and leakage rate.

Starved Lubrication of Elliptical EHD Contacts

Abstract: This paper focuses on the lubrication behavior of starved elliptical Elasto-HydroDynamic (EHD) contacts. Starvation is governed by the amount of lubricant available in the inlet region and can result in much thinner films than occurring under fully flooded conditions. Therefore, it would be desirable to be able to predict the onset and severity of starvation and to be able to relate film reduction directly to the operating conditions and lubricant properties. The aim of this work is to explore the influence of these parameters on starvation. A combined modeling and experimental approach has been employed. The numerical model has been developed from an earlier circular contact study [1]. In this model, the amount and distribution of the lubricant in the inlet region determines the onset of starvation and predicts the film decay in the contact. Numerical simulations for a uniform layer on the surface show that a single parameter, characteristic of the inlet length of the contact in the fully flooded regime, determines the starved behavior. Film thickness measurements under starved conditions were performed to validate this theory. For a circular contact excellent agreement was found. In theory the same mechanism applies to elliptic contacts, however, the behavior is more complicated.

Cage Instabilities in Cylindrical Roller Bearings

Abstract: A six-degree-of-freedom model was developed and used to simulate the motion of all elements in a cylindrical roller bearing. Cage instability has been studied as a function of the roller-race and roller-cage pocket clearances for light-load and high-speed conditions. The effects of variation in inner race speed, misalignment, cage asymmetry, and varying size of one of the rollers have been investigated. In addition, three different roller profiles have been used to study their impact on cage dynamics. The results indicate that the cage exhibits stable motion for small values of roller-race and roller-cage pocket clearances. A rise in instability leads to discrete cage-race collisions with high force magnitudes. Race misalignment leads to a rise in instability for small roller-cage pocket clearances since skew control is provided by the sides of the cage pocket. One roller of larger size than the others causes inner race whirl and leads to stable cage motion for small roller-race clearances without any variation in roller-cage pocket clearance. Cage asymmetry and different roller profiles have a negligible impact on cage motion.

A Surface Wear Prediction Methodology for Parallel-Axis Gear Pairs

Abstract: In this study, a surface wear prediction methodology for spur and helical gears is proposed. The methodology employs a finite elements-based gear contact mechanics model in conjunction with the Archard’s wear formulation to predict wear of contacting tooth surfaces. An iterative numerical procedure is developed to account for the changes in the gear contact as the gears wear. A methodology is developed to import gear coordinate measurement machine data into the gear contact model in order to analyze gears with actual manufactured surfaces with profile and lead modifications. Results of an experimental study are presented for validation of the methodology. A set of simulations is also included to highlight the differences between gear pairs having modified and unmodified tooth surfaces, with and without manufacturing errors in terms of their wear characteristics. @DOI: 10.1115/1.1691433#

Wear-Rate Uncertainty Analysis

Abstract: Wear due to relative motion between component surfaces is one of the primary modes of failure for many engineered systems. Unfortunately, it is difficult to accurately predict component life due to wear as reported wear rates generally exhibit large scatter. This paper analyzes a reciprocating tribometer in an attempt to understand the instrument-related sources of the scatter in measured wear rates. To accomplish this, an uncertainty analysis is completed for wear-rate testing of a commercially available virgin polytetrafluoroethylene pin on 347 stainless steel counterface. It is found that, for the conditions selected in this study, the variance in the experimental data can be traced primarily to the experimental apparatus and procedure. Namely, the principal uncertainty sources were found to be associated with the sample mass measurement and volume determination.

Granular Lubrication: Toward an Understanding of the Transition Between Kinetic and Quasi-Fluid Regime

Abstract: This paper is devoted to the understanding of flow characteristics of granular lubrication. The regimes of interest are: the kinetic regime in which collisions between particles are essentially binary and the quasi-fluid regime in which the duration of particle-to-particle contact is longer, primarily due to compaction. For this purpose, a quasi-two-dimensional particle dynamic simulation package is developed. The contact parameters between particles are chosen in order to mimic kinetic simulations. These contact laws are also valid in the quasi-fluid regime. The predictions of the particle dynamic simulations are compared to those obtained using the kinetic model. Good agreement between the two approaches is demonstrated. Furthermore, it is shown how the flow transition between the kinetic and the quasi-fluid regime can be determined. The influence of parameters that affect the transition is studied. The magnitude of the area fraction, on the order of about 90 percent of that of a hexagonal closest packing, seems to be the main factor that determines this transition.

Hydrodynamic Analysis of Compliant Foil Bearings With Compressible Air Flow

Abstract: A model is developed to predict the hydrodynamic performance of a foil journal bearing. The model accounts for both the compressibility of air and the compliance of the bearing surface. A series of predictions of the load-carrying capacity based on the numerical solution for pressure is presented that cover a wide range of operating speeds. The results show good agreement with existing experimental data.@DOI: 10.1115/1.1739242#

A Systems Approach to the Solid Lubrication of Foil Air Bearings for Oil-Free Turbomachinery

Abstract: Foil air bearings are self-acting hydrodynamic bearings which rely upon solid lubricants to reduce friction and minimize wear during sliding which occurs at start-up and shut-down when surface speeds are too low to allow the formation of a hydrodynamic air film This solid lubrication is typically accomplished by coating the non-moving foil surface with a thin, soft polymeric film The following paper introduces a systems approach in which the solid lubrication is provided by a combination of self lubricating shaft coatings coupled with various wear resistant and lubricating foil coatings The use of multiple materials, each providing different functions is modeled after oil-lubricated hydrodynamic sleeve bearing technology which utilizes various coatings and surface treatments in conjunction with oil lubricants to achieve optimum performance In this study, room temperature load capacity tests are performed on journal foil air bearings operating at 14,000 rpm Different shaft and foil coating technologies such as plasma sprayed composites, ceramic, polymer and inorganic lubricant coatings are evaluated as foil bearing lubricants The results indicate that bearing performance is improved through the individual use of the lubricants and treatments tested Further, combining several solid lubricants together yielded synergistically better results than any material alone

Measurement of Tangential Contact Hysteresis During Microslip

Abstract: This paper describes a measurement system designed to determine the hysteresis that develops between two surfaces as a result of small-amplitude tangential relative motion. Hysteresis is determined by measuring the tangential force and relative displacement of the contacting surfaces as they oscillate. These measurements also produce values of contact parameters such as friction coefficient and tangential contact stiffness. Although these parameters depend on the tribological properties, most of them also exhibit strong sensitivity to measurement errors. The measurement system described here avoids or at least reduces many of the measurement artifacts. This paper validates the measurement system by analyzing and estimating potential errors and describes corrections to systematic errors where possible.

Adhesion and Friction Studies of Silicon and Hydrophobic and Low Friction Films and Investigation of Scale Effects

Abstract: Tribological properties are crucial to the reliability of microelectromechanical systems/ nanoelectromechanical systems (MEMS/NEMS). In this study, adhesion and friction measurements are made at micro and nanoscales on single-crystal silicon (commonly used in MEMS/NEMS) and hydrophobic and low friction films. These include diamondlike carbon (DLC), chemically bonded perfluoropolyether (PFPE), and self-assembled monolayer (SAM) films. Since MEMS/NEMS devices are expected to be used in various environments, measurements are made at a range of velocities, humidities, and temperatures. The relevant adhesion and friction mechanisms are discussed. It is found that solid films of DLC, PFPE, and SAM can reduce the adhesion and friction of silicon. These films can be used as and-adhesion films for MEMS/NEMS components under different environments and operating conditions. Finally, the adhesion and friction data clearly show scale dependence. The scale effects on adhesion and friction are also discussed in the paper.

Changes of Surface Topography During Running-In Process

Abstract: This study investigated the surface topographical changes during running-in. A theoretical model, which is composed of Johnson translatory system and a microscopic wear model, was used to describe the changes of surface roughness during running-in for general surfaces. Running-in tests were conducted for engine bores with different surface height distributions in order to understand surface topographical changes and validate the theory. Experimental results show that the theoretical model provides a good indication of changes of surface topography for surfaces with different types of initial height distributions.

Elasto-Plastic Normal Contact of Three-Dimensional Fractal Surfaces Using Halfspace Theory

Abstract: The elasto-plastic normal contact of fractal surfaces is investigated. To study the influence of several surface parameters like fractal dimension and resolution, the surfaces are numerically generated using a special form of the structure function which is motivated by measurements of real rough surfaces. The contact simulation uses an iterative elastic halfspace solution based on a variational principle. A simple modification allows also the approximative solution of elasto-plastic contact problems. The influence of different surface parameters is studied with respect to the load-area relationship and the load-gap relationship. The simulations show that for realistic surface parameters the deformation is always in the plastic range.

Rotordynamic-Coefficient and Leakage Characteristics for Hole-Pattern-Stator Annular Gas Seals—Measurements Versus Predictions

Abstract: Selected test results are presented for an annular gas seal using a smooth rotor and a hole-pattern-roughness stator for a supply pressure of 70 bar, three pressure ratios, three speeds up to 20,000 rpm, two clearances, and three preswirl ratios. Dynamic data include frequency-dependent direct and cross-coupled stiffness and damping coefficients. Static data include leakage and upstream and downstream pressures and temperatures. Very good agreements are found between measurements and predictions from a two-control-volume bulk-flow model.

Experimental and Three-Dimensional Finite Element Study of Scratch Test of Polymers at Large Deformations

Abstract: An experimental and numerical study of the scratch test on polymers near their surface is presented. The elastoplastic response of three polymers is compared during scratch tests at large deformations: polycarbonate, a thermosetting polymer and a sol-gel hard coating composed of a hybrid matrix (thermosetting polymer-mineral) reinforced with oxide nanoparticles. The experiments were performed using a nanoindenter with a conical diamond tip having an included angle of 30 deg and a spherical radius of 600 nm. The observations obtained revealed that thermosetting polymers have a larger elastic recovery and a higher hardness than polycarbonate. The origin of this difference in scratch resistance was investigated with numerical modelling of the scratch test in three dimensions. Starting from results obtained by Bucaille (J. Mat. Sci., 37, pp. 3999-4011, 2002) using an inverse analysis of the indentation test, the mechanical behavior of polymers is modeled with Young's modulus for the elastic part and with the G'sell-Jonas' law with an exponential strain hardening for the viscoplastic part. The strain hardening coefficient is the main characteristic parameter differentiating the three studied polymers. Its value is equal to 0.5, 4.5, and 35, for polycarbonate, the thermosetting polymer and the reinforced thermosetting polymer, respectively. Firstly, simulations reveals that plastic strains are higher in scratch tests than in indentation tests, and that the magnitude of the plastic strains decreases as the strain hardening increases. For scratching on polycarbonate and for a penetration depth of 0.5 μm of the indenter mentioned above, the representative strain is equal to 124%. Secondly, in agreement with experimental results, numerical modeling shows that an increase in the strain hardening coefficient reduces the penetration depth of the indenter into the material and decreases the depth of the residual groove, which means an improvement in the scratch resistance.

Mixed Lubrication Analyses by a Macro-Micro Approach and a Full-Scale Mixed EHL Model

Abstract: This paper presents an improvement of a simplified approach, namely, the macro-micro approach, used to model the mixed elastohydrodynamic lubrication problems in counter-formal contacts, and its comparison with Zhu and Hu's full-scale mixed-EHL model. In this approach, Patir and Cheng average flow model is employed to obtain the distribution of piecewise average pressure. A contact-embedment method that incorporates the detail of asperity contact pressure into the overall pressure distribution is utilized to reveal the severity of surface interaction. Numerical experiments are conducted, and the results are compared with those obtained by means of the full-scale mixed-EHL. The regime of the application of this macro-micro approach is explored.

Sealability of Stationary Metal-to-Metal Seals

Abstract: The effectiveness of stationary metal-to-metal seals is investigated with respect to contact pressure and length, load history, and the use of sealing compounds. Laboratory cup and cone tests were carried out, and experimental results were used to develop a sealability criterion. A sealability parameter is proposed and a critical value for it was obtained from experiments. The criterion was validated through full-scale tests of tubular connections and FEA. This criterion can be used for the comparison, qualification and future performance improvements of different metal-to-metal seals, in particular those used in the petroleum industry.

A Computer Thermal Model of Mixed Lubrication in Point Contacts

Abstract: This paper presents a transient thermal model for mixed lubrication problems in point contacts. The model deterministically calculates pressure and surface temperature by simultaneously solving a system of equations that govern the lubrication, contact and thermal behaviors of a point contact interface. The pressure distribution on the entire computation domain is obtained through solving a unified Reynolds equation system without identifying hydrodynamic or asperity contact regions. The point heat source integration method is applied to determine the temperature distributions on contact surfaces. The interactions between pressure and temperature are considered through incorporating viscosity-temperature and density-temperature relations in the Reynolds equation, then solving the equation system iteratively. With the successful implementation of an FFT-based algorithm (DC-FFT) for calculation of surface deformation and temperature rise, the numerical analysis of lubricated contact problems, which used to involve a great deal of computation, can be performed in acceptable time. The model enables us to simulate various lubrication conditions, from full film elastohydrodynamic lubrication (EHL) to boundary lubrication, for a better understanding of the effect of surface roughness. Numerical examples are analyzed and the results show that the present model can be used to predict pressure and surface temperature over a wide range of lubrication conditions, and that the solution methods are computationally efficient and robust.

Homogenization of the Generalized Reynolds Equation for Ultra-Thin Gas Films and Its Resolution by FEM

Abstract: We address the numerical modeling of roughness or texture effects in ultra-thin gas films. Rarefaction (high Knudsen number) effects are dealt with using the Generalized Reynolds Equation, and a homogenization procedure is proposed to rigorously account for arbitrary roughness/texture shapes. The presentation is focused on head-disk magnetic storage devices, but the techniques proposed are general. Some details of the implementation, along with numerical tests, are included. By removing the small space and time scales from the problem, the methodology allows for efficient modeling of slider bearings with small-scale features.

Mechanical and Thermomechanical Elastic-Plastic Contact Analysis of Layered Media With Patterned Surfaces

Abstract: An elastic-plastic finite element analysis of a sphere in normal and sliding contact with a layered medium possessing a patterned surface with regularly spaced rectangular pads was conducted in order to investigate the effect of pattern geometry on the contact pressure distribution and subsurface stress-strain field. Three-dimensional sliding simulations were performed for lateral displacement of the indenting sphere approximately equal to two times the pad spatial periodicity. Three complete loading cycles, involving indentation, sliding, and unloading of a rigid sphere, were simulated to assess the effect of repeated sliding on the stresses in the first (hard) layer and plastic deformation in the underlying (soft) layer Thermomechanical sliding contact simulations of an elastic-plastic layered medium with a patterned surface and an elastic-plastic sphere with properties identical to those of the first layer were carried out to examine the effect of frictional heating on the deformation behavior of the medium. Results are presented for the temperature distribution and maximum temperature variation at the surface and the evolution of subsurface plasticity in terms of Peclet number The likelihood of thermal cracking in the wake of microcontacts during sliding is interpreted in the context of the thermal tensile stress due to the temperature gradients in the layered medium.

A Granular Dynamic Model for the Degradation of Material

Abstract: The work presented here is a model of the degradation of a material (by particle detachment), based on a two dimensional granular dynamic model designed to study the flows of third body particles inside a contact. As the detached particles (third body) cannot exit the contact, the detachments stop after a certain time and a stable layer of third body can be seen. It is shown that the thickness of this stable layer depends both on the conditions applied (normal pressure and sliding speed) and the physicochemical interactions between the detached particles. Such investigations provide better understanding of the mechanism leading to the degradation of material.

Comparison of homogenization and direct techniques for the treatment of roughness in incompressible lubrication

Abstract: Homogenization is a formal mathematical two-scale averaging process that can be applied to roughness problems and can replace previous heuristic averaging procedures, which have sometimes led to ambiguous results This procedure was previously mathematically developed and applied to compressible flow problems The purpose of this paper is the development of a special form of Reynolds equation for such homogenized conditions applied to the incompressible Newtonian case The equation allows the calculation of the operating characteristics of a contact by taking into account the local geometry of surfaces while making a substantial improvement in computing time The method allows for the study of rough surfaces, but requires considerably fewer calculated points than for traditional deterministic discretization methods

Combining and Contacting of Two Rough Surfaces with Asymmetric Distribution of Asperity Heights

Abstract: The statistical approach of describing rough surfaces is extended to include the contact oftwo rough surfaces in which their distribution of asperity heights can either be symmetricor asymmetric, and the asymmetry is modeled using the normalized Weibull distribution.In considering the contact between two rough surfaces, as in most practical applications,the contact can be approximated by an equivalent rough surface in contact with a smoothplane. The roughness parameters of the equivalent surface are obtained using the spectralmoment method, and its validity is verified using realistic surface roughness measure-ments. This paper presents a method to obtain the equivalent rough surface with a Weibulldistribution of asperity heights, in which the standard deviation and skewness parametersof asperity heights of the actual contacting surfaces are preserved. The advantages of thismethod are demonstrated via direct comparisons with a previously proposed method aswell as with exact numerical simulation of the contact parameters of several differentactual surfaces from magnetic storage and MEMS applications. For practical engineeringapplications, where the roughness parameters of each individual surface are known,contour plots for the skewness value of the equivalent rough surface are provided forpractical ranges of combinations of standard deviation ratios and skewness values. Asexpected when the roughness of one of the contacting surfaces dominates, the skewness issolely determined by the rougher surface. @DOI: 10.1115/1.1614822#

Actual Eyring Models for Thixotropy and Shear-Thinning: Experimental Validation and Application to EHD

Abstract: The Eyring sinh law is presently the most well-accepted model for shear-thinning of EHD lubricants at high pressure. It was, however, not accepted for this purpose by Eyring, who found it to be of only limited usefulness for thixotropy. Then, it is extremely important that these models receive a critical review using data obtained by modern methods to evaluate the actual Eyring models and show how they differ from the model in use today. Data from high-pressure viscometers were used to validate the actual Eyring models. The Ree-Eyring model for shear-thinning obeys time-temperature-pressure superposition. A film thickness calculation shows it to suffer from the same anomalous behavior in sliding contact as does the sinh law.

Efficient Modeling of Fretting of Blade/Disk Contacts Including Load History Effects

Abstract: Fretting is a frictional contact phenomenon that leads to damage at the contact region between two nominally-clamped surfaces subjected to oscillatory motion of smallamplitudes The region of contact between the blade and the disk at the dovetail joint is one of the critical locations for fretting damage The nominally flat geometry of contacting surfaces in the dovetail causes high contact stress levels near the edges of contact A numerical approach based on the solution to singular integral equations that characterize the two-dimensional plane strain elastic contact of two similar isotropic surfaces presents itself as an efficient technique to obtain the sharp near-surface stress gradients associated with the geometric transitions Due to its ability to analyze contacts of any two arbitrary smooth surfaces and its computational efficiency, it can be used as a powerful design tool to analyze the effects of various factors like shape of the contact surface and load histories on fretting The calculations made using the stresses obtained from the above technique are consistent with the results of the experiments conducted in the laboratory

On the Significance of Thermal and Deformation Effects on a Plain Journal Bearing Subjected to Severe Operating Conditions

Abstract: The present work analyzes the influence of global and local thermal effects and also mechanical and thermal deformations on bearing performance. Local thermal effects are important in the case of a highly loaded bearing because these effects are concentrated within a small zone of the bearing. The thermoelastohydro-dynamic study, including deformations due to pressure, leads to a significant decrease in maximum pressure and a slight decrease in maximum temperature. For accurate performance predictions of bearings operating under severe conditions, numerical simulations have to take into account local thermal effects and both mechanical and thermal deformations.

Waviness Deformation in Starved EHL Circular Contacts

Abstract: 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.

Granular Flow Lubrication: Continuum Modeling of Shear Behavior

Abstract: Because at extreme temperatures, conventional liquid lubrication breaks down, researchers have proposed using flows of solid particles as a lubricating mechanism. The particles may be powders, which tend to coalesce and slide over one another in sustained contact, or granules, which collide with one another in fluctuating motion. Distinction between these two regimes is elucidated. The behavior of various granular flows is studied using a granular kinetic lubrication (GKL) model. Our GKL model is a continuum approach that applies proper rheological constitutive equations for stress, conduction and dissipation to thin shearing flows of granular particles, as well as the most rigorous boundary conditions for momentum and energy transport. A robust numerical code, utilizing Newton's finite differencing method, is developed to apply GKL theory to the problem of simple shearing flow. The code solves two second-order, coupled nonlinear ordinary differential equations with coupled boundary conditions of the first-order. As a result, new parametric curves for the local flow properties of the large-particle granular flows are constructed. Results from the GKL model agree qualitatively with past experiments using glass granules in an annular shear cell.

Adhesion forces for sub-10 nm flying-height magnetic storage Head Disk Interfaces

Abstract: A quasi-dynamic adhesion model is used to calculate the intermolecular adhesion forcespresent in ultra low flying Head Disk Interfaces (HDI’s). The model is a continuum-basedmicromechanics model that accounts for realistic surfaces with roughness, molecularlythin lubricants, and is valid under both static and dynamic sliding conditions. Severaldifferent levels of surface roughness are investigated ranging from extremely smoothsurfaces having a standard deviation of surface heights s52 A to rougher interfaces withseveral nanometer roughness. It is found that when the flying-height is greater than 5 nm,there are no significant adhesive forces, whereas for flying-heights less than 5 nm, adhe-sion forces increase sharply, which can be catastrophic to the reliability of low flyingHDI’s. In addition to roughness, the apparent area of contact between the flying recordingslider and the magnetic disk is also found to significantly affect the magnitude of theadhesion forces. The adhesion model is validated by direct comparisons with adhesion‘‘pull-off’’ force measurements performed using an Atomic Force Microscope with con-trolled probe tip areas and magnetic disks having different lubricant thickness.@DOI: 10.1115/1.1645299#