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Abstract:  As non-traditional applications of hard disk drives emerge, their mechanical robustness during the operating state is of greater concern. A procedure for simulating the shock responses of a disk-suspension-slider air bearing system is proposed in this paper. A finite element model of the system is developed and modified, and it is used to obtain the dynamic normal load and moments applied to the air bearing slider. The dynamic load and moments are then used as input data for the air bearing dynamic simulator to calculate the dynamic flying attitudes. We obtain not only the responses of the structural components, but also the responses of the air bearing slider. The procedure is convenient for practical application, because it separates the work into two essentially uncoupled steps. It is used to simulate the shock response of a drive. The system modeled is linear if the load dimple of the suspension maintains contact with the slider, but it is non-linear if the dimple separates due to a strong shock. The air bearing has different responses for upward and downward shocks. Slider-asperity contacts occur when a strong shock is applied.

Abstract: In this paper we present an upwind higher order finite volume numerical scheme over unstructured triangular mesh to solve the slider air bearing problem of hard disk drives. The scheme is nodal based, which uses the median dual as the control volume. The convection part of the generalized Reynolds equation is modeled by the flux difference splitting technique. Higher order accuracy in space is achieved by a linear reconstruction technique with a flux limiting technique incorporated to prevent oscillation in the high-pressure gradient regions. A linear Galerkin method is used to discretize the diffusion terms. In addition, a non-nested multi-grid iteration technique is used to increase the convergence rate. Finally, the steady state flying attitude of a slider subject to pre-applied suspension force and torques is obtained by a Quasi–Newton iteration method, and the results of this scheme are compared with two other schemes.

An experimental modal analysis system, which has been shown to be effective in the study of small structures, is utilized to analyze the interaction of the disk and the suspension assembly in a computer disk drive. A thorough understanding of the interaction of these structures is obtained by determining the modal parameters for each of the components in an uncoupled state and in a coupled state with the disk both stationary and rotating. It is shown that when a natural frequency of the suspension is close to that of the disk, two system resonant frequencies are created when the components are coupled together.

The axisymmetric elastostatic problem of a cracked sphere embedded in a dissimilar matrix is solved by using the solution for a spherical cavity in an infinite medium together with the axisymmetric solution for a cracked sphere given in the companion paper in this issue of the Journal of Applied Mechanics, Pages 538-544. Numerical results are presented for (a) interface stress for various composites (b) dependence of the stress-intensity factor on the material parameters and ratios of crack to sphere radii, (c) the difference in the elastic strain energy for a cracked and uncracked composite.

The problem of a cracked sphere is solved with the use of Boussinesq stress functions. Two coordinate systems—oblate spheroidal for representing the crack surface and spherical polars for the spherical surface—are used to satisfy boundary conditions. Integral representations and transformations of harmonic functions are used to relate stress functions in the two coordinate systems. This procedure leads to a system of algebraic equations which is solved, for axisymmetric tractions on both the surfaces. Graphical results are presented for one specific loading case.

The prospect of contact and near-contact recording in magnetic hard disk files naturally leads to reduced flying heights of the read-write head over the rigid disk. To avoid dry contact at these low head-to-disk spacings, a lubricant should be used to minimize wear and maximize reliability. Since fluids generally have a much greater viscosity than air and very large shear rates develop under the slider, it is believed that a fully flooded interface can only be practically possible if the fluid possesses a non-Newtonian character with a significant amount of shear-thinning. In this paper, we present results from extensive numerical simulations of the fully flooded head-disk interface using the finite element technique. This approach has proven very successful in calculating a wide variation of slider geometries for various fluid nonlinearities.

The problem of plane steady vibration of an elastic wedge of arbitrary angle (less than 180 degrees) subject to harmonic normal and shearing tractions on its faces is reduced to a system of singular integral equations by the superposition of two half-plane solutions. The integral equations have kernels with Cauchy singularities of a non-translation type, except for the 90 degree wedge. The locations of these singularity lines are shown graphically as a function of wedge angle.

The problem is reduced to a single Fredholm integral equation by using a superposition of two half-plane solutions. The treatment is exact within the theory of linear elastodynamics. Dissipation is introduced in the form of linear viscous damping at the surface in order to overcome the mathematical difficulties which are associated with the nondecaying surface waves that occur when no dissipation is present.

In a previous paper (Chen and Bogy, 1992) we studied the effects of various load parameters, such as friction force, transverse mass, damping, stiffness and the analogous pitching parameters, of a stationary load system in contact with the spinning disk on the natural frequencies and stability of the system when the original eigenvalues of interest are well separated. This paper is a follow-up investigation to deal with the situations in which two eigenvalues of the freely spinning disk are almost equal (degenerate) and strong modal interactions occur when the load parameters are introduced. After comparing an eigenfunction expansion with the finite element numerical results, we find that for each of the transverse and pitching load parameters, a properly chosen two-mode approximation can exhibit all the important features of the eigenvalue changes. Based on this two-mode approximation we study the mathematical structure of the eigenvalues in the neighborhood of degenerate points in the natural frequency-rotation speed plane. In the case of friction force, however, it is found that at least a four-mode approximation is required to reproduce the eigenvalue structure. The observations and analyses presented provide physical insight into the modal interactions induced by various load parameters in a spinning disk-stationary load system.

The reflection coefficient is derived for an isotropic, homogeneous elastic layer of arbitrary thickness that is perfectly bonded to such an elastic half-space of a different material for the case when plane waves are incident from an inviscid fluid onto the layered solid. The derived function is studied analytically by considering several limiting cases of geometry and materials to recover previously known results. Approximate reflection coefficents are then derived using various plate models for the layer to obtain simpler expressions that are useful for small values of σd, where σ is the wave number and d is the layer thickness. Numerical results based on all the models for the propagation of interface waves localized near the fluid-solid boundary are obtained and compared. These results are also compared with some previously published experimental measurements.

The dynamic loading process in hard disk drives is simulated numerically. The effects of the slider’s loading velocity and initial pitch and roll on its dynamics during loading, as well as on slider-disk contacts, are studied by using the dynamic loading simulator. The air bearing forces due to the squeezing and shearing flows are calculated and their contributions to the dynamics of the slider during loading are investigated. Slider-disk contacts are considered in the numerical simulation through generalized impulse-momentum equations. Slider-disk contact criteria are obtained from the numerical simulation, and they are compared with those obtained from a previous experimental parameter study.

The parameters that appear to determine if slider-disk contact occurs during dynamic loading are the relative loading velocity at the instant of load and the initial pitch and roll of the slider at its unloaded state. A dual-beam LDV system is employed in this study to measure the displacement, pitch, and roll during dynamic loading for five different standard 3380-type sliders in order to investigate the effects of the initial pitch and roll. The effects of the initial height and control loading speed are also examined by using the dual-beam LDV and acoustic emission (AE). Based on the experimental results, we propose several slider-disk contact criteria. Among them, the criterion based on the initial diagonal slope and the peak loading velocity gives a simple way to predict if slider-disk contacts will occur, but it overlooks the effect of the signs of the initial pitch and roll. A three-dimensional criterion based on the peak velocity and the initial pitch and roll angles appears to be more reliable. Using either criterion, it is found that high peak loading velocity causes slider-disk contact, and sliders with larger initial pitch or roll angles are more likely to hit the disk.

Scanning Tunneling Microscopy is used to modify and measure the surface of magnetic media disks. A very rugged diamond tip allows continued scanning after it has severely scratched or punched the surface. Three techniques are used. First a manual method of penetrating the surface using a stand-alone head makes a scratch of essentially uncontrollable length and depth. Then the normal head is used to cause surface penetration by removing the bias voltage while scanning. Better control is obtained as regards the location and depth of the indentation. Excellent control of indentation location and depth can be obtained by using a new software developed by the STM manufacturer to push the tip into the surface with the piezoelectric scanner. The control of the indentations and their subsequent measurement may make the STM a useful tool as a hardness tester for ultra-thin films, on the order of a few tens of nanometers.

In many studies of sliding interfaces, the measurement of friction is complicated by quasi-harmonic vibrations of the transducer system. An analytical technique is introduced which accounts for the dynamic characteristics of a force transducer under periodic excitation, and is used to compute the forcing function in the sliding interface. The force transducer is modeled as an elastic cantilever-beam with an attached rigid mass. The forcing function is obtained by solving the time-dependent, fourth-order partial differential equation of Euler-Bernoulli beam theory. The solution is facilitated by the application of Fourier series expansions in time and eigenfunction expansions in space. Results of the method are compared to previous analyses of friction-induced vibration in which the elasticity of the transducer is modeled as a simple spring and the rigid body as a lumped mass, leading to a single degree-of-freedom (DOF) governing equation. It is found that a single DOF calculation based on instantaneous measurement of displacement agrees surprisingly well with the results of the Euler-Bernoulli analysis. A single DOF model based on instantaneous measurement of strain and a static displacement-strain calibration factor agrees well with the Euler-Bernoulli analysis for a low frequency range but deviates at higher frequencies.

Friction tests on thin film magnetic disks with carbon overcoats were performed using commercial read/write heads as sliders. The results provide evidence that the thin film overcoats wear through chemical means in the presence of gaseous oxygen, and through mechanical means in the absence of oxygen. When small concentrations of water are present, friction behavior resembling that of an oxidizing environment is observed, suggesting oxidation of the carbon film preceded by dissociation of adsorbed water.

This two part paper presents the experimental observation and numerical simulation of the dynamic response of self-acting gas-lubricated slider bearings used to maintain the sub-micron spacings between the Read/Write transducers and the rotating disks in magnetic recording disk files. In this Part II, a factored implicit finite difference scheme is used to integrate the Reynolds lubrication equation, which describes the isothermal compressible fluid flow within the bearing region, and a fourth order Runge-Kutta method is used to solve the equations of motion, which describe the slider dynamics. Using this numerical model, the theoretical slider response due to a rectangular step in the disk surface is obtained. Excellent correlation is observed between theory and experiment. Results are presented to illustrate the effects of step size, step location, and surface velocity on the dynamic performance of slider bearings.

This two part paper presents the experimental observation and numerical simulation of the dynamic response of self-acting gas-lubricated slider bearings used to maintain the sub-micron spacings between the Read/Write transducers and the rotating disks in magnetic recording disk files. In this Part I, a novel laser Doppler interferometric technique is used to measure the transient motions of the R/W head as it encounters an artificially introduced crater-like surface imperfection and a sputtered rectangular step.

Several perfluoropolyether (PFPE) lubricants are evaluated in terms of their ability to maintain low friction and resist wear. The lubricants tested include three nonpolar liquid lubricants and one polar liquid lubricant. Dynamic friction measurements are presented for an IBM 3380-type slider in contact with 130 mm carbon-coated thin film disks. Disk surface run-in and disk durability are evaluated by monitoring the friction force during constant speed sliding. Disk run-in is presented as a function of lubricant thickness and sliding speed, while disk durability is determined for different disk topographies and lubricant thicknesses. It was found that lubricant viscosity was well correlated with the amount of disk run-in and the number of sliding cycles until disk failure. It is proposed that the greater wear durability of the less viscous lubricants can be attributed to their greater mobility on the disk surface.

Static and dynamic friction coefficients are presented for an Al2O3·TiC slider in contact with 130 mm carbon-coated rigid thin film disks lubricated with several different perfluoropolyether lubricants. The lubricants tested include three nonpolar liquid lubricants and one polar liquid lubricant with dihydroxyl end groups. The effects of lubricant film thickness, disk surface topography, sliding speed and lubricant viscosity are investigated. In many cases, the interfaces exhibited a sharp increase in the dynamic and static friction coefficients after a certain film thickness was reached, due to strong adhesion in the interface. In most cases, the lubricant thickness for the onset of high friction forces was found to increase with increasing disk surface roughness, lubricant viscosity and sliding speed. Under certain conditions stick/slip of the slider occurred during which the static friction increased with time of contact. The various data suggest that the rate at which strong adhesion develops depends on the lubricant viscosity.

This paper is a continuation of Part I, which considers numerical models for the various components of the HDA. Here the solvers are coupled and the resulting numerical simulator is used to study the slider-disk spacing variation that occurs when a slider passes a bump on the disk. The results are compared with a simpler simulator and it is found that new information is obtained here that illustrates the role of suspension resonances in slider-disk spacing. We also study slider-disk spacing variations due to track accessing for both linear and rotary actuators. Finally we conduct a similar study for the problem of actuator crash stop. Of particular interest is the way in which the spacing variation depends on steady flying height. Low flying sliders have stiffer air bearings, which excite more suspension resonances. On the other hand, these sliders have less spacing change during track accessing and crash stop compared to higher flying sliders.

In previous papers the dynamics of air bearing sliders used to carry the read/write transducers in magnetic hard disk files has been studied. These studies are useful in evaluating the steady flying and stability of sliders subjected to various disturbances. They are particularly useful in finding the natural frequencies of the air bearings. However, in hard disk drives the sliders are attached to suspensions, which are highly specialized structures that connect the sliders to the positioning actuators. These suspensions have to be relatively stiff in lateral translation, but very flexible in pitch and roll. This latter feature is accomplished by the gimbal or flexure that connects the slider to the end of the suspension. The suspension-gimbal structure has its own natural frequencies, which can be excited by disturbances such as track seeking and impacting the actuator against the crash stop. In order to study the effect of these structures on the head-disk spacing it is necessary to include them in the numerical simulator. In this two part study such a simulator is developed. In Part I the component parts and their interfaces are modeled. In Part II the numerical simulation of the coupled system is accomplished and the numerical results of several sample simulations are presented and discussed.

An improved DMT adhesion model is used in conjunction with an elastoplastic contact model to analyze the adhesion of contacting rough solid surfaces covered with extremely thin layers of a lubricant having a very high affinity for the surfaces. This we call sub-boundary lubrication. The paper investigates the effects of the solid surface topography and the film thickness of the lubricant on the adhesion and pull-off forces. A roughness-dependent critical thickness phenomenon is predicted: very rough surfaces may exhibit low adhesion for a wide range of lubricant thicknesses, while for smooth surfaces adhesion may increase dramatically even for a film thickness t below the standard deviation of surface heights σ. The increased adhesion could cause the surfaces to stick together to the extent that sensitive tribological systems may be damaged.

Although friction force measurements using one sensor to detect both the normal deflection and rotation angle of a scanning probe are convenient and popular, the critical issues regarding the calibration of the instruments have not been fully studied. A Lateral Force Microscope (LFM), modified from the Point Contact Microscope (PCM), is used to simultaneously measure the surface topography and friction force. An optical head is used to measure the normal bending deflection and rotation angle of the cantilever that carries the diamond tip. Emphasis is put on the development of reliable calibration procedures for obtaining the normal deflection and rotation sensitivities of the optical head as well as the spring constants in the bending and torsion modes. The friction loop, which is essential for friction measurements, is investigated in detail. The LFM is used to measure a two-phase composite to show its ability to distinguish different materials on a surface. Wear tests on a single-crystal silicon <100> surface show different friction coefficient regimes, depending on the applied load. For small loads, there is no wear and the friction coefficient is constant. For larger loads, the friction coefficient and wear depth increase with normal load.

Microscopic friction and wear were measured on both the original top surfaces and freshly worn surfaces of three solid materials including a silicon wafer, a Mn-Zn ferrite block and an Au film, using a recently developed scanning probe microscope with sharp diamond tips. A critical point was observed on the friction versus normal loading force curve. The critical point divides the friction curve into two distinct regimes: a low friction regime in which the friction coefficients are from 0.03–0.06, and a high friction regime where the friction coefficients are between 0.12 and 0.38 depending on the materials tested and the tips. The critical loads at the critical points are different for different materials and different tips. But the average pressures corresponding to the critical points calculated by the Hertz elastic contact theory for different tips are close to each other for the same material. The freshly worn surfaces have tribological behaviors similar to those of the corresponding original top surfaces. Below the critical load no wear is detectable, whereas above the critical load wear is obtained with the wear depth proportional to the load. The implications are that a no-wear sliding condition is possible, for example in contact recording systems, if the asperity contact loads all remain less than the critical value for the particular sliding system.

In a Lateral Force Microscope (LFM), appropriate spring constants of the tip assembly are essential for obtaining proper normal loads for wear or scratch tests and good lateral force signals. We developed a new tip assembly design for which the lateral and normal springs can be changed independently. It was installed on a LFM where two optical heads are used to detect the lateral and normal deflections of the tip assembly for simultaneous measurements of the surface topography and friction force. Reliable calibration procedures for the LFM are presented. The LFM was used to measure the lateral forces in wear tests under various normal forces for thin film magnetic disks with and without a carbon overcoat. The friction coefficient is constant in the load range where there is no wear and increases with normal load after the tip starts to damage the surface. The carbon-coated disk has a lower friction coefficient and can support larger normal loads without wear.

A numerical scheme based on the finite difference technique is developed to simulate the steady-state flying conditions and dynamic responses of subambient pressure sliders with shaped rails. In order to suppress numerical difficulties caused by the clearance discontinuities present in the subambient pressure sliders, the control volume formulation of the linearized generalized lubrication equation is utilized. For the shaped rail sliders, a method of averaging the mass flow across the rail boundaries is implemented. Furthermore, the power-law scheme by Patankar, is implemented in calculating the mass flows. The resulting equation is solved using the alternating direction implicit method. For the simulation of steady-state flying conditions, a variable time step algorithm is implemented for the purpose of reaching the steady-state values as quickly as possible. This numerical scheme is very efficient in that the coarse finite difference mesh is sufficient for numerical stability, and that the time step changer very much improves the convergence rate. The static flying heights of the Transverse Pressure Contour and the “Guppy” slider are calculated for different disk velocities and slider skew angles. For the Guppy slider, the dynamic responses of the slider to a cosine bump and disk runout are simulated.

A numerical scheme based on the finite difference technique is developed to simulate the steady-state flying conditions and dynamic responses of subambient pressure sliders with shaped rails. In order to suppress numerical difficulties caused by the clearance discontinuities present in the subambient pressure sliders, the control volume formulation of the linearized generalized lubrication equation is utilized. For the shaped rail sliders, a method of averaging the mass flow across the rail boundaries is implemented. Furthermore, the power-law scheme by Patankar, is implemented in calculating the mass flows. The resulting equation is solved using the alternating direction implicit method. For the simulation of steady-state flying conditions, a variable time step algorithm is implemented for the purpose of reaching the steady-state values as quickly as possible. This numerical scheme is very efficient in that the coarse finite difference mesh is sufficient for numerical stability, and that the time step changer very much improves the convergence rate. The static flying heights of the Transverse Pressure Contour and the “Guppy” slider are calculated for different disk velocities and slider skew angles. For the Guppy slider, the dynamic responses of the slider to a cosine bump and disk runout are simulated.

The prospect of contact and near-contact recording in magnetic hard disk files naturally leads to reduced flying heights of the read-write head over the rigid disk. To avoid dry contact at these low head-to-disk spacings, a lubricant should be used to minimize wear and maximize reliability. Since fluids generally have a much greater viscosity than air and very large shear rates develop under the slider, it is believed that a fully flooded interface can only be practically possible if the fluid possesses a non-Newtonian character with a significant amount of shear-thinning. In this paper, we present results from extensive numerical simulations of the fully flooded head-disk interface using the finite element technique. This approach has proven very successful in calculating a wide variation of slider geometries for various fluid nonlinearities.

In Part I, the multiple contact region solutions for an axisymmetric indenter were presented. The solution technique utilized integral transforms and singular integral equations. The emphasis there was the study of the conditions of contact as a function of the physical parameters of the indenter and the layered elastic half space. The method and results were similar to those for the analogous plane-strain problem that was studied in Shield and Bogy (1989). However, several differences in detail were required for the analysis of the axisymmetric geometry. In this Part II, the solution of Part I is used to study some related problems that have been considered previously in the literature for homogeneous half spaces. First we solve the problem of the axisymmetric annular indenter for the layered half space. Multiple contact region solutions are studied and the problem of an axisymmetric punch with internal pressure is solved for the layered half space and also for the special case of a layer with a traction-free lower surface. Finally, the problem of an annular crack in a homogeneous or layered structure is solved.

The contact of a flat, simply-connected axisymmetric indenter with a layered elastic half space is examined. The problem is mathematically formulated using integral transforms to derive singular integral equations for the contact pressure. The solution of these equations is obtained by expansion in orthogonal polynomials. The solution predicts complete contact between the indenter and the surface of the layered half space only for a restricted range of the material and geometrical parameters. Outside of this range, solutions exist with multiple contact regions. A parameter space is divided into zones for single and multiple contact solutions and comparisons are made with the solutions for the analogous plane-strain problem.

The plane-strain problem of a smooth, flat rigid indenter contacting a layered elastic half space is examined. It is mathematically formulated using integral transforms to derive a singular integral equation for the contact pressure, which is solved by expansion in orthogonal polynomials. The solution predicts complete contact between the indenter and the surface of the layered half space only for a restricted range of the material and geometrical parameters. Outside of this range, solutions exist with two or three contact regions. The parameter space divisions between the one, two, or three contact region solutions depend on the material and geometrical parameters and they are found for both the one and two layer cases. As the modulus of the substrate decreases to zero, the two contact region solution predicts the expected result that contact occurs only at the corners of the indenter. The three contact region solution provides an explanation for the nonuniform approach to the half space solution as the layer thickness vanishes.

A rod with a lumped mass attached to its trailing end travels axially with a uniform velocity and strikes an elastic half space that is covered with an adhering viscoelastic layer. The problem is reduced to integral equations for the average contact stress and the displacement of the rod tip into the contact surface. The kernels of these integral equations are composed of temporal Green’s functions for the rod and the layered half space, which represent the response of each to an impulsive uniform normal traction. The Green’s function for the rod is obtained in closed form, while that for the layered half space is obtained through a numerical Laplace transform inversion. The integral equations are solved numerically with a second-order stable scheme. Solutions are computed for a wide variety of materials and configurations, providing the stress and displacement history, as well as the stress-displacement response. The results show the effects of changes in rod material and length, lumped mass, layer material, substrate material, and viscoelastic material parameters.

The effect of head-disk impacts due to repeated dynamic load is investigated experimentally. Loading conditions more severe than those typically found in ramp-load disk drives are applied to ensure that contacts occur, and disk-synchronized head loading motions are applied so that the head-disk contact points are all distributed within a small area on the disk. The resulting readback signal decrease was observed to correlate with the head-disk impact velocity and hence the slider’s vertical approaching velocity. With a larger vertical velocity, readback signal decrease appeared earlier and the amount of decrease was larger. The results indicate that dynamic load-unload should be quite reliable under typical loading conditions, and the reliability of dynamic load-unload can be achieved by controlling the vertical approaching velocity of the slider. This is comparatively easier than controlling the narrow manufacturing tolerances of the slider’s pitch and roll of the head-suspension assembly. The technological trend toward using smaller-sized head-suspension assemblies and higher-coercivity magnetic disks may further enhance the dynamic load head-disk interface durability.

Experiments and finite element simulations are presented pertaining to the effective hardness and the mechanics of indentation and sliding contact on elastic-plastic layered media. Hardness measurements obtained from scratch experiments are presented for thin-film rigid disks with 30 nm carbon overcoats. Reproducible results are obtained for residual scratch depths greater than approximately 8 nm. A simple force balance model is used to calculate the effective hardness of the layered medium. Hardness values for the surface layer are calculated by fitting a relationship between the hardness, scratch geometry, and layer thickness to the experimental data. The experimental results are compared with three-dimensional finite element simulations of a rigid spherical indenter sliding over a half-space with a stiffer and harder surface layer. The finite element results are used to verify the hardness model applied to the experimental data and to provide insight into the observed experimental behavior in the context of the associated elastic-plastic deformation characteristics of the layered medium.

A scanning probe microscope with a 80 nm radius diamond tip was used to investigate the wear resistance of single-crystal silicon and N+-implanted silicon. The N+ implantation conditions were 35 to 150 keV and 5 × 1016 ions/cm2. The N+ concentration depth profile was analyzed by using secondary ion mass spectrometry, and the chemical structure of N+-implanted silicon was also analyzed by using x-ray photoelectron spectroscopy. The following results were obtained. The maximum N+ concentration on the ion-implanted silicon shifted further below the surface and the thickness of the high ion concentration region increased with the implantation energy. The high N+ concentration region using multiple energies of 35–150 keV during the same ion implantation process was wider than that for the N+-implanted silicon using a single energy. The wear resistance of ion-implanted silicon was higher than that of single-crystal silicon. The N+-implanted silicon using multiple energies during the same ion implantation process showed higher wear durability than that of the N+-implanted silicon using a single energy. The Si2p spectrum of the high N+ concentration region implied a structure similar to a Si3N4 film, which resulted in higher wear resistance.

A numerical simulation of slider-disk contact in a magnetic hard disk drive is studied using the Hertzian contact model. The slider-disk contact is caused by flying height fluctuation due to disk runout for very low flying sliders. The rough disk topography is generated numerically by combining a sinusoidal waviness and a Gaussian roughness. For each asperity contact, the radius of curvature is calculated from the disk topography, and the radius is used to calculate the contact force using the Hertzian contact model. The slider’s response to a single asperity calculated using the Hertzian contact model agrees well with the result obtained using the impulse-momentum based contact model. The simulation results of slider-disk contact including suspension dynamics are calculated with and without friction for a “nano-slider.”

In order to estimate the contact stress and deformation at the instant of head-disk impact during dynamic loading, Hertz’s impact theory is implemented in a dynamic loading numerical simulator. By using a finite difference model for the air bearing, a finite element model for the slider-flexure-suspension system, and Hertz’s contact model of head-disk impact, we obtain estimates of contact stress, area and time through simulation of the dynamic loading process. With our choice of the material properties and geometric configurations, the duration of sliding contact is about 7 μs, the maximum width of contact is about 10 μm, and the maximum contact stress is about 620 MPa. This is below the yield stresses of the chosen media.

Although friction force measurements using one sensor to detect both the normal deflection and rotation angle of a scanning probe are convenient and popular, the critical issues regarding the calibration of the instruments have not been fully studied. A Lateral Force Microscope (LFM), modified from the Point Contact Microscope (PCM), is used to simultaneously measure the surface topography and friction force. An optical head is used to measure the normal bending deflection and rotation angle of the cantilever that carries the diamond tip. Emphasis is put on the development of reliable calibration procedures for obtaining the normal deflection and rotation sensitivities of the optical head as well as the spring constants in the bending and torsion modes. The friction loop, which is essential for friction measurements, is investigated in detail. The LFM is used to measure a two-phase composite to show its ability to distinguish different materials on a surface. Wear tests on a single-crystal silicon <100> surface show different friction coefficient regimes, depending on the applied load. For small loads, there is no wear and the friction coefficient is constant. For larger loads, the friction coefficient and wear depth increase with normal load.

Microscopic friction and wear were measured on both the original top surfaces and freshly worn surfaces of three solid materials including a silicon wafer, a Mn-Zn ferrite block and an Au film, using a recently developed scanning probe microscope with sharp diamond tips. A critical point was observed on the friction versus normal loading force curve. The critical point divides the friction curve into two distinct regimes: a low friction regime in which the friction coefficients are from 0.03–0.06, and a high friction regime where the friction coefficients are between 0.12 and 0.38 depending on the materials tested and the tips. The critical loads at the critical points are different for different materials and different tips. But the average pressures corresponding to the critical points calculated by the Hertz elastic contact theory for different tips are close to each other for the same material. The freshly worn surfaces have tribological behaviors similar to those of the corresponding original top surfaces. Below the critical load no wear is detectable, whereas above the critical load wear is obtained with the wear depth proportional to the load. The implications are that a no-wear sliding condition is possible, for example in contact recording systems, if the asperity contact loads all remain less than the critical value for the particular sliding system.

In a Lateral Force Microscope (LFM), appropriate spring constants of the tip assembly are essential for obtaining proper normal loads for wear or scratch tests and good lateral force signals. We developed a new tip assembly design for which the lateral and normal springs can be changed independently. It was installed on a LFM where two optical heads are used to detect the lateral and normal deflections of the tip assembly for simultaneous measurements of the surface topography and friction force. Reliable calibration procedures for the LFM are presented. The LFM was used to measure the lateral forces in wear tests under various normal forces for thin film magnetic disks with and without a carbon overcoat. The friction coefficient is constant in the load range where there is no wear and increases with normal load after the tip starts to damage the surface. The carbon-coated disk has a lower friction coefficient and can support larger normal loads without wear.

Several perfluoropolyether (PFPE) lubricants are evaluated in terms of their ability to maintain low friction and resist wear. The lubricants tested include three nonpolar liquid lubricants and one polar liquid lubricant. Dynamic friction measurements are presented for an IBM 3380-type slider in contact with 130 mm carbon-coated thin film disks. Disk surface run-in and disk durability are evaluated by monitoring the friction force during constant speed sliding. Disk run-in is presented as a function of lubricant thickness and sliding speed, while disk durability is determined for different disk topographies and lubricant thicknesses. It was found that lubricant viscosity was well correlated with the amount of disk run-in and the number of sliding cycles until disk failure. It is proposed that the greater wear durability of the less viscous lubricants can be attributed to their greater mobility on the disk surface.

Static and dynamic friction coefficients are presented for an Al2O3·TiC slider in contact with 130 mm carbon-coated rigid thin film disks lubricated with several different perfluoropolyether lubricants. The lubricants tested include three nonpolar liquid lubricants and one polar liquid lubricant with dihydroxyl end groups. The effects of lubricant film thickness, disk surface topography, sliding speed and lubricant viscosity are investigated. In many cases, the interfaces exhibited a sharp increase in the dynamic and static friction coefficients after a certain film thickness was reached, due to strong adhesion in the interface. In most cases, the lubricant thickness for the onset of high friction forces was found to increase with increasing disk surface roughness, lubricant viscosity and sliding speed. Under certain conditions stick/slip of the slider occurred during which the static friction increased with time of contact. The various data suggest that the rate at which strong adhesion develops depends on the lubricant viscosity.

This paper is a continuation of Part I, which considers numerical models for the various components of the HDA. Here the solvers are coupled and the resulting numerical simulator is used to study the slider-disk spacing variation that occurs when a slider passes a bump on the disk. The results are compared with a simpler simulator and it is found that new information is obtained here that illustrates the role of suspension resonances in slider-disk spacing. We also study slider-disk spacing variations due to track accessing for both linear and rotary actuators. Finally we conduct a similar study for the problem of actuator crash stop. Of particular interest is the way in which the spacing variation depends on steady flying height. Low flying sliders have stiffer air bearings, which excite more suspension resonances. On the other hand, these sliders have less spacing change during track accessing and crash stop compared to higher flying sliders.