The homogenization process of the Reynolds equation describing compressible liquid flow

This paper summarizes the homogenization process of rough, hydrodynamic lubrication problems governed by the Reynolds equation used to describe compressible liquid flow. Here, the homogenized equation describes the limiting result when the wavelength of a modeled surface roughness goes to zero. The lubricant film thickness is modeled by one part describing the geometry/shape of the bearing and a periodic part describing the surface topography/roughness. By varying the periodic part as well as its wavelength, we can try to systematically investigate the applicability of homogenization on this type of problem. The load carrying capacity is the target parameter; deterministic solutions are compared to homogenized by this measure. We show that the load carrying capacity rapidly converges to the homogenized results as the wavelength decreases, proving that the homogenized solution gives a very accurate representation of the problem when real surface topographies are considered.     

Film height optimization of dynamically loaded hydrodynamic slider bearings

A method is presented to determine the optimal surface shape distribution for a hydrodynamic slider bearing. This is the surface shape distribution that is able to carry a prescribed load while maintaining a maximum separation between the surfaces. This method is first derived for a bearing with constant load and sliding speed. It is subsequently extended for a bearing with periodic load and sliding speed. Results for slider bearings with different shapes, loads and speeds are presented. It is shown that the numerical procedure developed in this paper is numerically more efficient than a reference optimization method.     

Friction reduction in low-load hydrodynamic lubrication with a hydrophobic surface

A novel tribometer capable of measuring low friction forces and low loads at high speeds has been employed to measure the friction coefficient in a pure sliding, ball-on-flat contact in hydrodynamic lubrication conditions. The tribometer was custom-built for measuring friction at low loads, to allow the authors to investigate the feasibility of using the liquid-slip phenomenon for the lubrication of high-sliding MEMS. The theory behind lubrication with liquid slip and its effect on friction is briefly discussed. Contacting surfaces were treated to create hydrophobic/hydrophilic or hydrophilic/hydrophilic pairs. Hydrophobic surfaces were made by coating mica with a self-assembled silane monolayer while the hydrophilic surfaces used were freshly cleaved mica and plasma-cleaned steel. Experiments were conducted at sliding speeds of up to 2 m/s and loads below 0.2 N. An aqueous glycerol solution was used as lubricant. Results obtained with hydrophilic/hydrophilic surfaces were in accord with hydrodynamic lubrication theory. Tests with hydrophobic/hydrophilic surfaces revealed a reduction in friction, which may be attributed to lubricant slip against the hydrophobic surface.     

规则形貌作用下非牛顿流体润滑的数值分析

利用Navier-Stockes方程和有限体积法,求解斜面滑块润滑模型的承载力和摩擦力,研究形貌高度较大时,表面形貌影响下非牛顿介质的润滑效果,获得用传统的包含表面形貌统计模型的雷诺方程方法难以获得的流场的细节信息。数值结果显示：在规则横向条纹形貌的作用下,形貌突变处出现压力突变;当形貌高度大于1%油膜厚度时才对润滑结果有较大影响,承载力和压差阻力随形貌高度的增加而增加,摩擦阻力随之下降,总阻力基本保持不变;当形貌高度大于油膜厚度的10% 时,摩擦阻力随之上升,总阻力迅速增加。非牛顿介质幂律模型参数对润滑结果的影响远大于形貌参数的影响,但其并不影响承载力等结果随形貌高度变化的趋势,选择合适的润滑材料参数是改善润滑的关键因素。     

On the hydrodynamic lubrication analysis of piston rings

A theoretical hydrodynamic lubrication analysis of piston rings is presented. A numerical scheme is developed to solve the Reynolds' equation and the load equilibrium equation simultaneously. The hydrodynamic effects are examined in detail by considering solutions to the problem of lubricating the top compression ring in a two-stroke diesel engine. The minimum film thickness is computed throughout a complete cycle. The pressure profiles and film shapes at different crankshaft angles are presented. In the method proposed, the camtation boundary condition within the lubricated conjunction is included in the analysis.     

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.     

Fluid film lubrication in the presence of cavitation: a mass-conserving two-dimensional formulation for compressible,piezoviscous and non-Newtonian fluids

A mass-conserving formulation of the Reynolds equation has been recently proposed by some of the authors to deal with cavitation in lubricated contacts [1]. This formulation, based on the mathematical derivation of a linear complementarity problem (LCP), overcomes the drawbacks previously associated with the use of such complementarity formulations for the solution of cavitation problems in which reformation of the liquid film occurs. In the present paper, the methodology favoured in [1], already successfully applied to solve textured bearing and squeeze problems in the presence of cavitation in a one dimensional domain for incompressible fluids, has been extended to include the effects of fluid compressibility, piezoviscosity and the non-Newtonian fluid behaviour and it has been also applied to the analysis of two dimensional problems. The evolution of the cavitated region and the contact pressure distribution are studied for a number of different configurations which can be considered as relevant benchmarks.In particular, some of the results obtained with the proposed scheme are critically analysed and compared with the predictions obtained using alternative formulations, including full CFD calculations. The stability of the proposed algorithm and its flexibility in terms of implementation of different models for compressibility, piezoviscosity and non-Newtonian behaviour are highlighted.     

Hydrodynamic lubrication of textured steel surfaces under reciprocating sliding conditions

The influence of surface topography on lubricant film thickness has been investigated for the reciprocating sliding of patterned plane steel surfaces against cylindrical counterbodies under conditions of hydrodynamic lubrication. Patterns of circular depressions, grooves and chevrons were used, and the fractional area coverage, depth, width and sliding orientation relative to the texture were systematically varied. Textured samples with features much larger than the elastic contact width gave film thicknesses, which were smaller than those for non-textured samples. This effect was more significant for larger features. For patterns composed of circular pockets, maximum film thickness was achieved for an area coverage fraction f≈0.11. Chevron patterns pointing along the sliding direction gave higher film thicknesses than those pointing across. For an area coverage ratio of ca. 0.06, maximum film thickness was achieved for a feature depth to width ratio of about 0.07. Among the patterns investigated, chevrons were the most effective and grooves the least effective in increasing hydrodynamic film thickness.     

Full film lubrication of deep drawing

An analytical model for full film lubrication of deep drawing is developed, combining the elastic–plastic membrane finite element code of deep drawing together with full film lubrication theory. In full film lubrication, the surfaces are not in contact, and the gap in between includes two types of lubrication: the thick film lubrication regime and the thin film lubrication regime. The film thickness and the strain distribution of full film lubrication are predicted here. The theoretical results show excellent agreement with the experiment data.     

A computer model of mixed lubrication in point contacts

A numerical model of mixed lubrication is presented in this paper. The idea introduced here is that asperity contact may be viewed as a result of a continuous decrease in film thickness, so that the transition between contact and non-contact is continuous and the same mathematical model should work for both regions. The pressure over the thin films is assumed to obey the Reynolds equation, and the solution of the equation, under the condition of h→0, is expected to be the same as that predicted by the theory of elasticity. To achieve convergent and stable solutions, the left-hand side terms of the Reynolds equation are switched off when the local film thickness approaches zero, leading to a reduced Reynolds equation. Pressure distributions over the entire computation domain are thus obtained through solving a unified equation system without identifying hydrodynamic or asperity contact regions. Computations were conducted for several example cases and results show that convergent solutions are achievable on different types of roughness, over a wide range of λ ratios (0.01 to infinity), and for different slide-to-roll ratios (0.0–2.0).     

Analysis of the nonlinear behavior of gear pairs considering hydrodynamic lubrication and sliding friction

This paper describes an analysis of the nonlinear behavior of gear pairs according to the direct contact elastic deformation model over a wide range of speeds, considering the hydrodynamic effects and friction force. The inclusion of the hydrodynamic effect facilitates nonlinearity by increasing the overlap range (i.e., multiple solution regimes) and damping, as well as decreasing elastic deformation and tooth reaction forces. The effects of various lubrication parameters, such as viscosity and film width, on the nonlinear dynamic behavior were analyzed. While the viscosity has a strong effect on the behavior of gear pair systems, friction has very little effect on torsional behavior. Although the model of direct contact without friction has overall nonlinear behavior similar to the model including hydrodynamic effects with friction, the time data of these models are different due to the squeeze effect. This paper was recommended for publication in revised form by Associate Editor Eung-Soo Shin Cheon Gill-Jeong received his B.S. in Mechanical Engineering from Seoul National University (SNU), Korea, in 1981. He then received his M.S. and Ph.D. degrees from SNU in 1983 and 1988, respectively. He served as a senior research engineer at Seoul National University Hospital and Daewoo Heavy Industry for several years. Dr. Cheon is currently a Professor at the Division of Mechanical Engineering at Wonkwang University in Iksan, Korea. His research interests include dynamics, tribology, and design engineering.     

Thin film hydrodynamic lubrication of flying heads in magnetic disk storages

Typical hydrodynamic lubrication problems commonly encountered in the ultrathin spacing between a computer flying head and a magnetic disk are reviewed. In magnetic disk storages, minimizing the spacing between the head and disk is essential to promote the largest possible increase in magnetic bit density. In the small (nearly 1.0 μm) spacing that has recently been attained, the rarefaction effects owing to the molecular mean free path become dominant. Specifically, in this paper the three governing equations resulting from the first- and second-order slip-flow models and from the linearized Boltzmann equation are compared. Next, some numerical approaches to eliminating the instability in pressure distribution in the high bearing number region are described. Surface roughness effects are also a principal concern in thin spacing. A mixed lubrication model which enables the analysis of the start/stop operation and the average film thickness theory for one- and two-dimensional roughnesses is summarized. Finally, from the viewpoint of practical head design, the slider dynamic characteristics and related slider design factors are discussed.     

The effect of texture shape on the friction coefficient and stiffness of gas-lubricated parallel slider bearings

Surface texturing is used to increase hydrodynamic pressure and reduce friction and wear between gas-lubricated parallel sliding surfaces in a variety of applications. The shape, geometry, and density of the patterned microtexture features (“dimples”) play a key role in the tribological performance of textured slider bearings. In this paper we evaluate the friction coefficient and stiffness of gas-lubricated textured parallel slider bearings as a function of six different texture shapes. The texture geometry and density are optimized in terms of minimum friction coefficient and maximum bearing stiffness for each individual texture shape, and then compared relative to each other. The ellipsoidal shape is found to yield the minimum friction coefficient and the highest bearing stiffness, independent of the operating conditions.     

On the steady-state performance of misaligned hydrodynamic journal bearings lubricated with micropolar fluids

The present work deals with the micropolar lubrication theory to the problem of the steady-state characteristics of hydrodynamic journal bearings considering two types of misalignment, e.g. axial (vertical displacement) and twisting (horizontal displacement). Using a finite difference method, the steady-state film pressures are obtained by solving modified Reynolds equation based on the micropolar lubrication theory. With the help of the steady-state film pressures, the steady-state performance characteristics in terms of load-carrying capacity, misalignment moment and friction parameter of a journal bearing are obtained at various values of eccentricity ratio, degree of misalignment and micropolar fluid characteristic parameters viz. coupling number and non-dimensional characteristic length.     

A study on the effect of starvation in mixed elastohydrodynamic lubrication

The effect of starvation in mixed elastohydrodynamic lubrication (EHL) regime is studied. Numerical simulations are conducted for both line and point (elliptical) contacts with the consideration of the surface roughness. The degree of starvation is linked directly to the reduction in the lubricant mass flow rate. Results are presented to gain insight on the influence of starvation on the film thickness as well as the interaction between the surface asperities. Extensive sets of simulation results are used to quantify the effect of starvation in the EHL of rough surfaces. Expressions are developed to predict the percentage of the load carried by the surface asperities (asperity load ratio) as well as the reduction of the central and minimum film thickness in the starved mixed EHL.     

Frequency-domain analysis of non-Newtonian fluid behavior in head-disk interface lubrication

A lubricant in a head-disk interface is considered as a non-Newtonian fluid. Properties of non-Newtonian lubricants are specified by three nonlinear functions and a modified Reynolds equation is derived for the varied film thickness in the interface. The shear dependent viscosity is the principal factor and it is expressed by a first order transfer function. Its amplitude frequency response describes the process of the viscosity variation and indicates that the shear dependent viscosity is affected not only by the lubricant material parameters, but also by the shear frequency. Based on the modified Reynolds equation, the numerical result of lubrication is given. The load capacity is not always higher or always lower than that of the Newtonian fluid. The effect of the first normal stress difference is enlarged with the slider flying height varies.     

On thin film lubrication

Various phenomena are revealed under EHL and micro-EHL conditions, such as the properties of the lubricant under high pressure, traction, and the load-bearing capacity of the lubricant film, and are discussed in the present paper. A new lubrication regime, thin film lubrication, has been discussed. The theoretical and practical significance of research on thin film lubrication is elaborated. Finally, the characteristics describing thin film lubrication and its main research directions are suggested.     

Linear stability analysis of hydrodynamic journal bearings under micropolar lubrication

The dynamic characteristics of hydrodynamic journal bearings lubricated with micropolar fluids are presented. The modified Reynolds equation is obtained using the micropolar lubrication theory. Applying the first order perturbation of the film thickness and steady state film pressure, the dynamic characteristics in terms of the components of stiffness and damping coefficients, critical mass parameter and whirl ratio are obtained with respect to the micropolar property for varying eccentricity ratios and slenderness ratios. The results show that micropolar fluid exhibits better stability in comparison with Newtonian fluid.     

Analysis of the dynamics of a slider-crank mechanism with hydrodynamic lubrication in the connecting rod-slider joint clearance

The conventional slider-connecting rod-crank mechanism is widely applied in mechanical systems. The use of hydrodynamic bearings in the mechanism joints is of particular interest in reducing friction, mainly in special conditions of lubrication such as the connecting rod-slider joint. This bearing belongs to a class of bearings with alternating rotational motion. This paper proposes a mathematical model for this particular problem, considering the dynamics of the slider-connecting rod-crank system interacting with the lubrication phenomenon in bearings with alternating motion. Two models were used to analyze the dynamics of the system. The first model (by Eksergian Equation of Motion) represents the system when the connecting rod end is in contact with the bearing surface, assuming, in this condition, the same behavior as that of rigid bearings (without clearance). The second model (by Lagrange Method) represents the system when the connecting rod end is in the hydrodynamic lubrication mode in the slider bore clearance. In this condition, the slider moves in relation to the connecting rod, presenting a problem of multi-degrees-of-freedom. The mathematic model of hydrodynamic lubrication was introduced to obtain more realistic results of the system's dynamic behavior.