Rough Slider Research Articles

A comparative study of the Reynolds equation solution for slider and journal bearings with stochastic roughness on the stator and the rotor

In the present work, a novel solution of the Reynolds Equation for hydrodynamically lubricated bearings with stochastic roughness is presented. On the basis of stochastic analysis and theory, an advanced form of Reynolds-type Equation is derived. The proposed equation formulation, utilizing Stein’s Lemma to calculate variational derivatives of the pressure with respect to the roughness variables, presents some differences in comparison with the deterministic Reynolds Equation, as well as to other previously published approaches which consider the stochastic surface roughness. The proposed methodology is validated against relevant results in other literature works and applied to characterize the tribological performance of rough slider and journal bearings with different roughness profiles, over a wide range of bearing design and operational parameters.

Numerical Simulation of Rough Thrust Pad Bearing Under Thin-Film Lubrication Using Variable Mesh Density

A numerical simulation of rough slider bearing under thin-film lubrication using variable mesh density has been carried out. The current investigation deals with the effect of deterministic surface roughness patterns, such as triangular, sawtooth, square and sinusoidal roughness patterns and temperature on pressure and film thickness distribution. The nature and shape of roughness and temperature play a significant role in pressure generation, which in turn influences load capacity and frictional coefficient. It has been observed that variable mesh density takes around 25% less number of iterations compared to fixed mesh density. Among all roughness patterns, square roughness dominates the generated pressure. Elastic deformation of greater than 50 nm in bounding surfaces has been found to influence the film formation. Small pressure generated under piezoviscous elastic and thermo-piezoviscous elastic conditions was deficient in causing squeezing effect on lubricant, which suggests that bearing is operating under isoviscous elastic and thermo-viscous elastic conditions instead of piezoviscous elastic and thermo-piezoviscous elastic. Insensitivity in load capacity was observed for a smaller value of film thickness.

An analysis of hydrodynamic ferrofluid lubrication of an inclined rough slider bearing

The present study aims at analysing the effects of surface roughness, porosity and magnetic field on an inclined slider bearing. The slider bearings mainly are designed for supporting transverse load in an engineering system and enjoy a priority due to its physical wedge pressure generating mechanism. The ferrofluid is being used as lubricant which becomes strongly magnetised in the presence of external magnetic field in a plane inclined rough slider bearing with slip velocity. The earlier studies were related to ferrofluid lubrication based on Shliomis model and it was concluded that the adverse effect of surface roughness was reduced due to magnetisation under the influence of proactive slip parameter. In the present study a space dependent magnetic field of the form has been considered rather than sinusoidal type H2 = KL2 sin (πX). The analysis brings out some interesting results due to change in pattern of magnetic field strength. The pattern of variation of magnetic field considered in the present study contributes to an increase in pressure and load capacity by and load by our conventional lubricant i.e. as that of magnetised lubricant. One interesting finding reported here is that, the adverse effect of slip parameter, reported in earlier studies over load carrying capacity turns rather sinusoidal to be favourable which may be due to the pattern of variation of magnetic field considered in the present study.

Effects of friction reduction of micro-patterned array of rough slider bearing

Complex micro-scale patterns have attracted interest because of the functionality that can be created using this type of patterning. This study evaluates the frictional reduction effects of various micro patterns on a slider bearing surface which is operating under mixed lubrication. Due to the rapid growth of contact area under mixed lubrication, it has become important to study the phenomenon of asperity contact in bearings with a heavy load. New analysis using the modified Reynolds equation with both the average flow model and the contact model of asperities is conducted for the rough slider bearing. A numerical analysis is performed to determine the effects of surface roughness on a lubricated bearing. Several dented patterns such as, dot pattern, dashed line patterns are used to evaluate frictional reduction effects. To verify the analytical results, friction test for the micro-patterned samples are performed. From comparing the frictional reduction effects of patterned arrays, the design of them can control the frictional loss of bearings. Our results showed that the design of pattern array on the bearing surface was important to the friction reduction of bearings. To reduce frictional loss, the longitudinal direction of them was better than the transverse direction.

Analysis of Thermal Effects in a Long Porous Rough Slider Bearing

This paper analyses the thermal and roughness effects on different characteristics of long porous slider bearings numerically. The roughness is assumed to be stochastic, Gaussian randomly distributed, and viscosity is assumed to be temperature dependent. The cases of one-dimensional longitudinal and transverse roughness are considered. The irregular domain of the fluid due to roughness is mapped to a regular domain so that the numerical method can be easily applied. It is shown that the combined effect has a significant influence on the performance of the bearing. The impact of the influence depends on the type of roughness and the permeability of the porous matrix. For transverse roughness model it is seen that the combined effect enhanced the load carrying capacity when compared to that of thermal effect on smooth surface, and the opposite is true for longitudinal roughness. However, the load capacity of the bearing is decreased due to the combined effect compared to that of roughness effect for both types of roughness models.

Performance of a Ferrofluid Based Rough Parallel Plate Slider Bearing: A Comparison of Three Magnetic Fluid Flow Models

Efforts have been made to present a comparison of all the three magnetic fluid flow models (Neuringer-Rosensweig model, Shliomis model, and Jenkins model) so far as the performance of a magnetic fluid based parallel plate rough slider bearing is concerned. The stochastic model of Christensen and Tonder is adopted for the evaluation of effect of transverse surface roughness. The stochastically averaged Reynolds-type equation is solved with suitable boundary conditions to obtain the pressure distribution resulting in the calculation of load carrying capacity. The graphical results establish that for a bearing’s long life period the Shliomis model may be employed for higher loads. However, for lower to moderate loads, the Neuringer-Rosensweig model may be deployed.

A Comparison of Porous Structures on the Performance of a Slider Bearing with Surface Roughness in Couple Stress Fluid Film Lubrication

This paper presents the theoretical study and analyzes the comparison of porous structures on the performance of a couple stress fluid based on rough slider bearing. The globular sphere model of Kozeny-Carman and Irmay’s capillary fissures model have been subjected to investigations. A more general form of surface roughness is mathematically modeled by a stochastic random variable with non-zero mean, variance and skewness. The stochastically averaged Reynolds type equation has been solved under suitable boundary conditions to obtain the pressure distribution in turn which gives the expression for the load carrying capacity, frictional force and coefficient of friction. The results are illustrated by graphical representations which show that the introduction of combined porous structure with couple stress fluid results in an enhanced load carrying capacity more in the case of Kozeny-Carman model as compared to Irmay’s model.

Film Shape Optimization for Two-Dimensional Rough Slider Bearings

ABSTRACTA new approach was proposed in the present study for optimizing the film shape of rough slider bearings to obtain maximum load-carrying capacity under center of pressure demand. The average flow model was used to specify the effect of surface roughness on the Reynolds equation. The partial differential equations were solved using the multiphysics software COMSOL, and film shape was optimized with the method of moving asymptotes (MMA). The new method was compared with the existing work to validate its feasibility and accuracy. Effects of surface roughness patterns and size and shape of polynomial function degrees on the load-carrying capacity have been investigated and the optimum shapes and corresponding load-carrying capacity under different roughness patterns were acquired. The optimization results reveal that the new approach with combined COMSOL and MMA is effective in shape optimization for rough slider bearings. For a square bearing, the isotropic roughness pattern enhances load-carrying capacity most.

A complex systems analysis of stick-slip dynamics of a laboratory fault

We study the stick-slip behavior of a granular bed of photoelastic disks sheared by a rough slider pulled along the surface. Time series of a proxy for granular friction are examined using complex systems methods to characterize the observed stick-slip dynamics of this laboratory fault. Nonlinear surrogate time series methods show that the stick-slip behavior appears more complex than a periodic dynamics description. Phase space embedding methods show that the dynamics can be locally captured within a four to six dimensional subspace. These slider time series also provide an experimental test for recent complex network methods. Phase space networks, constructed by connecting nearby phase space points, proved useful in capturing the key features of the dynamics. In particular, network communities could be associated to slip events and the ranking of small network subgraphs exhibited a heretofore unreported ordering.

Tribological Applications Considering Roughness Effects on Grain Flow

The grain flow lubrication, based on Haff's grain flow theory and the Patir/Cheng flow factors method, is applied in the simulations of rough slider bearings and chemical mechanical polishing. In this paper, the results of flow factor, the performance of rough slider bearings and the mechanism of the CMP process for grain flow are briefly demonstrated. An improved CMP model, considering the partial hydrodynamic grain flow lubrication and elastic-plastic microcontact theory, is also proposed. The contact area ratio and the elastoplastic contact area ratio are presented to improve the understanding of CMP mechanisms.

Molecular Dynamics Simulation of Lubricant Redistribution and Transfer at Near-Contact Head-Disk Interface

When the spacing between the slider and lubricant in a hard disk drive decreases to less than 5 nm, the effect of the intermolecular force between these two surfaces can no longer be ignored. This effect on the lubricant distribution at the near-contact head disk interface is investigated via molecular dynamics method. In this study, the lubricant is confined between a smooth disk surface and a rough slider surface represented as a partially cosinusoidal wave. The simulation results reveal that the intermolecular force-induced meniscus formation at the near-contact head disk interface is strongly sensitive to the slider-to-disk separation, lubricant film thickness and the asperity shape (or roughness) of the slider. The attractive van der Waals forces between the slider and lubricant become weaker with increasing slider-to-disk separation and asperity mid-height, but decreasing lubricant film thickness and asperity mid-width. The Hamaker theory application to van der Waals interactions is also introduced to verify the molecular dynamics simulation. It is found that the critical separation, below which the lubricant will lose its stability to form a meniscus, increases approximately linearly with the lubricant film thickness, for slider surfaces with or without roughness both in the molecular dynamics simulation and Hamaker theory application to van der Waals interactions. Moreover, it is observed that the critical separation between a smooth disk and rough slider surface will slightly decrease when the asperity mid-height increases. The same phenomenon is observed when the asperity mid-width reduces.

Surface Roughness Effects on Air Bearing Performance Over a Wide Range of Knudsen and Wave Numbers

Design of a near contact air bearing interface such as that created by a recording head slider and data storage disk requires consideration of a lubrication equation that is appropriate for high Knudsen number flows. The Poiseuille flow database reported by Fukui and Kaneko, 1990 [“A Database for Interpolation of Poiseuille Flow Rates for High Knudsen Number Lubrication Problems,” ASME J. Tribol., 112, pp. 78–83] is appropriate over a wide range of Knudsen numbers and is used throughout the data storage industry for analysis of the low flying recording head slider air bearing. However, at such low clearances, the topography of the air bearing surfaces also comes into question, making it important to consider both rarefaction and surface roughness effects in the air bearing design. In order to simplify the air bearing analysis of rough surfaces, averaging techniques for the lubrication equation have been developed for situations where the number of roughness elements (or waves) is either much greater or much less than the gas bearing number. Between these two extremes there are currently no roughness averaging methods available. Although some analytical and numerical studies have been reported for continuum and first-order slip conditions with simple geometries, little or no results have appeared that include both surface roughness and high Knudsen number flows outside the limited ranges where surface averaging techniques are used. In order to better understand the influence of transverse surface roughness over a wide range of Knudsen numbers and the relationship of key parameters involved, this paper describes a primarily analytical air bearing study of a wide, rough surface slider bearing using the Poiseuille flow database reported by Fukui and Kaneko. The work is focused outside the limited ranges where current surface averaging methods for the lubrication equation are expected to be valid.

Property Analysis of the Rough Slider Bearings in Micromotors for MEMS Applications

Based on the kinetic theory of gases, a new slip model is applied for the gas-lubricated Rayleigh slider bearings beneath three bushings of a micromotor in microelectromechanical systems (MEMS). A modified Reynolds equation is established by taking into account of the coupling effects of gas rarefaction and roughness and then analytical solutions for pressure distribution, load-carrying capacity and its streamwise location, and velocity profile are obtained for various slider-bearing configurations. The new slip model is validated by comparisons with the results presented in other researcherspsila works. It is indicated that the present new slip model is of better accuracy in predicting the bearing properties than the first-order, second-order slip models, and modified molecular gas lubrication model and is a good approximation to variable hard sphere and variable soft sphere models. The solutions provided by the present new slip model match the solution obtained using the linearized Boltzmann equation very well. The results also show that the coupled effects of gas rarefaction and roughness are of great significance in the design of the bushings for slider bearings in micromotors.

Longitudinally rough slider bearings with squeeze film formed by a magnetic fluid

The effect of longitudinal surface roughness on the behaviour of slider bearing with squeeze film formed by a magnetic fluid has been analysed. The roughness of the bearing surface is modelled by stochastic random variable with non‐zero mean, variance and skewness. The concerned Reynolds' equation is stochastically averaged with respect to the random roughness parameter. Results for bearing performance characteristics such as load carrying capacity of the bearing, centre of pressure, frictional force and coefficient of friction for different values of α (mean), σ (standard deviation) and ε (measure of symmetry) are numerically computed. In order to investigate the quantitative effect of roughness on the performance characteristics, four shapes namely; plane slider, exponential slider, hyperbolic slider and secant slider for the lubricant film are considered. The results are presented in tabular form as well as graphically. It is observed that the bearing performance is significantly affected by all the three parameters characterizing the surface roughness.

Hydrodynamic lubrication of rough slider bearings with couple stress fluids

The combined effects of couple stresses and surface roughness on the performance characteristics of hydrodynamic lubrication of slider bearings with various film shapes, such as plane slider, exponential, secant and hyperbolic, are studied. A stochastic random variable with non-zero mean, variance and skewness is used to mathematically model the surface roughness of the slider bearing’s. The Stokes couple stress fluid model is used to characterize the rheological behavior of the lubricant with polymer additives. The modified expressions for the bearing characteristics, namely pressure, load carrying capacity, center of pressure, frictional force are obtained for the general lubrication film shape on the basis of Stokes microcontinuum theory for couple stress fluids. Results are computed numerically for various film shapes under consideration. It is observed that, for all the lubricant film shapes under consideration, the negatively skewed surface roughness increases the load carrying capacity, frictional force and temperature rise, while it reduces the coefficient of friction. On the contrary, the reverse trend is observed for positively skewed surface roughness. Further, these effects are more pronounced for the couple stress fluids.

Grain-flow lubrication of finite-width slider bearings with rough surfaces

In this paper, the average lubrication equation for grain flow is solved using a control volume method to analyze the performance of rough slider bearings. The effects of surface characteristics and film particle ratios under various slenderness ratios were investigated. The mean shear stress is derived in terms of shear stress factors. The effects of particle size are discussed and show that roughness effects are pronounced at smaller film particle ratios.

On the shape of the lubricant film for the optimum performance of a longitudinal rough slider bearing

Efforts have been made to study the optimum film profile for a longitudinally rough slider bearing. The roughness of the bearing surface is modelled by stochastic random variable with non‐zero mean, variance and skewness. The governing differential equation for lubricant pressure is the Reynolds equation which is stochastically averaged with respect to the random roughness parameter. The method of infinitesimal is used to determine the optimum lubricant film profile. Results for the step location, step height ratio and the bearing performance characteristics, such as load carrying capacity of the bearing, centre of pressure, frictional force and coefficient of friction for different values of α, σ and e, are numerically computed and tabulated. It is observed that the parameters α, σ and e characterizing the surface roughness of the bearing affect the bearing performance characteristics significantly.

Dynamics of rough slider bearings: effects of one-sided roughness/waviness

The paper discusses some dynamic effects of a sliding train of transversely oriented undulations on a rectangular bearing. It is shown that moving roughnesses or waviness may have a strong influence on important parameters of slider bearings, such as load capacity, friction force etc. The phenomenon discussed is caused by the change in the roughness phase with respect to the bearing extremities. The pressure generation is found to be dependent on this phase variation if the wavelengths are appreciable with respect to the bearing dimensions. The effects are therefore induced by waviness rather than by roughness.

A study of the film formation for a rough slider bearing

An average Reynolds equation, suggested by Patir and Cheng, is applied to the compound random surfaces, including both roughness and waviness, in the present paper. The critical load capacity W cr , at the moment when the minimum nominal film thickness h min = CR p , is regarded as the criterion to evaluate the film formation ability of nominally flat friction pairs. The important influence on the critical load capacity of the height profile of rough surfaces is demonstrated, i.e. W cr will increase rapidly as the values of a and R p / σ reduce. The critical load capacity of various slider bearings with different surface topographies is calculated and measured. The experimental results for the different specimens are similar to those predicted by the computer simulation. The significant effect of the height profile on film formation is confirmed by experiment. The simulation indicates that the good lubrication behaviour of wide scraped surfaces mainly results from the fact that they have smaller a and R p / σ characteristics, and a larger waviness component with longer wavelength.

Entrance and Stationary Roughness Effects on the Load Carrying Capacity of a Wide Wedge Gas Bearing

The objective of this work is the determination of the effects of surface roughness amplitude and inlet conditions on ultra-thin, compressible, isothermal, infinitely-wide gas bearings. The method of study is numerical in nature and consists of a second-order accurate finite difference solution of the Reynolds equation of lubrication without molecular slip for a range of bearing numbers spanning six orders of magnitude. The motivation for this work comes from the magnetic disk drive industry where ever decreasing head flying heights are being sought to increase the recording density. Past studies by these authors of the infinitely-wide air bearing with stationary roughness have shown that, unlike in the case of a smooth bearing, the load peaks at a finite bearing number comparable to that at which current rigid disk drives operate. This suggests that it may be possible to arrange the roughness pattern in such a way as to cause the slider to separate from the hard disk more rapidly, minimizing wear to both surfaces. A wedge bearing with stationary sinusoidal roughness is studied for different roughness amplitudes and two phases. It is shown that for all configurations considered, the load exhibits a peak unlike in the case of the smooth bearing where the load monotonically reaches a peak at an infinite gas bearing number. Two rough sliders with flat tapers smoothly attached to their leading edge are also studied to answer questions regarding the role that the inlet condition plays in the resulting magnitude and behavior of the generated load. The leading taper allows the bearing to dynamically determine the entrained flow rate and maximum pressure as well as to self prescribe the inlet condition at the leading edge of the first roughness wave. The inlet conditions prescribed by the developing flow in the flat taper region still give rise to a peak in the load. The addition of the smooth taper, however, causes an overall decrease (increase) in the load when the roughness waves are entirely above (below) the plane of the taper compared to the results of the rough bearing with no taper. It is demonstrated that all the considered roughness patterns result in a peak load at a finite bearing number. Of special interest are two bearing configurations: one composed of a smooth taper followed by a transversely roughened slider and the other is a rough slider with a transverse roughness pattern whose slope at the inlet of the bearing is negative. Both are shown to achieve a maximum lifting force at low bearing numbers, providing rapid separation while alleviating the narrow rail manufacturing problem.