Surface roughness effects on curved pivoted slider bearings with couple stress fluid

In this paper the effect of surface roughness on the performance of curved pivoted slider bearings is studied. A more general type of surface roughness is mathematically modelled by a stochastic random variable with nonzero mean, variance and skewness. The averaged modified Reynolds type equation is derived on the basis of Stokes microcontinuum theory for couple stress fluids. The closed‐form expressions for the mean pressure, load‐carrying capacity, frictional force and the centre of pressure are obtained. Numerical computations show that the performance of the slider bearing is improved by the use of lubricants with additives (couple stress fluid) as compared to Newtonian lubricants. Further, it is observed that the negatively skewed surface roughness increases the load‐carrying capacity and frictional force and reduces the coefficient of friction, whereas the positively skewed surface roughness on the bearing surface adversely affects the performance of the pivoted slider bearings. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Effect of surface roughness on static and dynamic characteristics of MHD couple stress lubrication of parabolic slider bearing

The effect of surface roughness on static and dynamic characteristics of parabolic slider bearing lubricated with couple stress fluid in the presence of magnetic field is theoretically analysed in this paper. The modified stochastic MHD couple stress Reynolds-type equation is derived on the basis of Christensen stochastic theory and considered two types of roughness pattern namely longitudinal and transverse. Expressions for steady pressure and load, dynamic stiffness and damping coefficients are obtained for both roughness patterns. Compared to smooth surface, transverse roughness pattern provides larger load-carrying capacity, dynamic stiffness and damping coefficients, whereas longitudinal roughness pattern has adverse effects. The presence of couple stress and applied magnetic field improves the bearing performance.     

Inertia Effects on Inclined Slider Bearings Lubricated by a Couple Stress Fluid

This article deals with a numerical investigation of fluid inertia effects on inclined slider bearings lubricated by couple stress fluids. Convective inertial forces are considered in the film fluid. A reduced version of the Navier-Stokes equations is thus derived. The non-Newtonian couple stress behavior of the lubricant is described based on the microcontinuum Stokes theory. The governing partial differential equations are discretized by finite differences based on boundary layer–type equations. The resulting algebraic equations are solved using a Gauss-Seidel method. Compared to the case of the non-inertia Newtonian lubricant, the couple effects of fluid inertia forces and non-Newtonian couple stresses provide a significant improvement in slider bearing load capacity.     

Coupled effects of surface roughness and flow rheology on elastohydrodynamic lubrication

The coupled effects of surface roughness and flow rheology on elastohydrodynamic lubrication (EHL) circular contact problems are analyzed and discussed. The averaged type Reynolds equation utilizing the average flow model on the interactions between couple stress fluids and surface roughness, the elastic deformation equation, the viscosity–pressure and density–pressure relations equations, and the force balance equation are solved numerically by the multilevel multi-integration (MLMI) algorithm to calculate the pressure distributions and film thickness shapes. The results show that the transverse type roughness and standard deviation of composite roughness enhance the pressure and film thickness in the central contact region. Moreover, the longer the characteristic length of the couple stress fluids is, the smaller the pressure distribution is in the central contact region and the greater the film thickness is in all regions.     

Inertial MHD Couple Stress Effects on Infinitely Wide Slider Bearings

This article presents a numerical study of magnetohydrodynamic (MHD) infinitely wide plane inclined slider bearings including both fluid inertia and non-Newtonian couple stress effects. Fluid inertia forces are considered in the film fluid using a simplified form of the Navier-Stokes equations. The non-Newtonian couple stress behavior of the lubricant is described based on the microcontinuum Stokes theory. The governing equations are discretized by finite differences using a boundary layer–type equations resolution. The resulting algebraic equations are solved using the Gauss-Seidel method. It is found that the couple effects of fluid inertia forces, MHD, and non-Newtonian couple stresses provide a significant improvement in the slider bearing load capacity compared to the case of the noninertia Newtonian nonconducting lubricant. The use of conducting lubricant diminishes the negative effect of inertia forces on the friction coefficient.     

Effect of bearing pad deformation on the performance of finite fixed-pad slider bearings

The load support and other performance characteristics of any bearing depend on its film thickness profile which can be significantly affected by elastic deformations. The effect of bearing surface deformation on the static performance of slider bearings is reported. Deformation of bearing pads was calculated by three-dimensional elasticity equations using a finite element method.To generalize the study, a non-dimensional deformation coefficient relating the geometrical parameters of bearing pad, the clearance space, the elasticity coefficient of the pad material, the lubricant viscosity and the velocity of the slider is defined. The static characteristics are calculated and compared for different values of the deformation coefficient. The effect of Poisson's ratio v of the pad material on the performance of a slider bearing for steel (v = 0.3) and brass (v = 0.4) as pad materials is reported.     

Hydrodynamic analysis of rough curved pivoted porous slider bearings with couple stress fluid

Abstract

The purpose of this paper is to study the effect of surface roughness on the performance of curved pivoted porous slider bearings lubricated with couple stress fluid. The modified B–J slip boundary condition is utilised at the porous/fluid film interface to derive the Reynolds type equation for the problem under consideration. To mathematically model the surface roughness due to non-uniform rubbing of bearing surfaces, a stochastic random variable with non-zero mean, variance and skewness is considered. The closed form solution is obtained for the averaged Reynolds equation, and the compact expressions for the mean fluid film pressure mean load carrying capacity, frictional force and the centre of pressure are obtained. The numerical computations of the results show the improved performance due to the couplestresses and the presence of negatively skewed surface roughness. However, the presence of porous facing and positively skewed surface roughness affects the performance of the pivoted porous slider bearing.     

The effects of surface irregularities on the performance characteristics of flexible finite journal bearings lubricated with couple stress fluids

A numerical solution for the elastohydrodynamic lubrication of finite journal bearings is presented. Couple stress effects resulting from blending the lubricant with various additives are considered. Elrod's cavitation algorithm, which automatically predicts film rupture and reformation in the bearings, is implemented in the solution scheme. A simple elastic model is used to describe the elastic deformation of the bearing liner. Furthermore, the effects of surface waviness on the performance of the bearing are incorporated into the analysis. A comprehensive study illustrates the effects of couple stress, liner flexibility, and surface waviness on the steady‐state performance of finite‐width journal bearings. The results show that these effects should be considered at higher values of the eccentricity ratio.     

超薄气体润滑磁盘／磁头系统动力学分析

应用修正后的雷诺方程描述超薄气体轴承的润滑特性,应用伽辽金近似建立气体轴承有限元法分析模型。使结构动力学模型与气体动力润滑模型有机地集成起来,建立了气体轴承-磁头结构的系统动力学模型。在考虑表面粗糙度对磁头飞浮稳定性影响时,引进方向模式参数以描述磁盘的表面形貌,仿真结果表明,粗糙表面能有效降低磁头瞬态响应时间,通过参数合理设计可阻止磁头的共振响应,粗糙度的方向特征对动力学的响应有一定的影响,但随着膜厚与粗糙峰高比率的增大,方向特征的影响将逐步降低。     

Contact-induced off-track vibrations of air bearing-slider-suspension system in hard disk drives

Contact-induced vibration of air bearing-slider-suspension system is a crucial issue for slider flying stability and head positioning precision of 1 Tbit/in² hard disk drives. In this paper, the contact-induced off-track vibrations of air bearing-slider-suspension system are investigated by simulation. A dynamic simulator is developed to calculate the interactions between the air bearing dynamics and vibrations of slider-suspension assembly. The simulation model consists of a finite element model of suspension assembly, an air bearing model based on the generalized lubrication equation, and a slider–disk contact model based on the probability distributions of surface roughness. A sequential method is used to couple all these models and analyses. The time history of the slider and suspension motions, together with the time-varying forces including air bearing force, air shear forces, contact force and friction force can be obtained. The effects of different contact conditions, such as the contact intensity, friction coefficient, and disk surface waviness on off-track vibrations are investigated numerically in details. The results reveal some mechanisms on how these factors contribute to the off-track vibrations of suspension assembly.     

Combined effects of surface roughness and couple stresses on static and dynamic behaviour of squeeze film lubrication of porous journal bearings

Abstract

The combined effects of surface roughness and the couple stresses on the static and dynamic characteristics of squeeze film lubrication in porous journal bearings with no journal rotation are theoretically studied. The Stokes couple stress fluid model is considered to model the lubricants with additives. The surface roughness on the porous journal bearing is mathematically modelled by a random variable with non-zero mean, variance and skewness. The generalised stochastic Reynolds type equation is derived for the problem under consideration. The applied load is considered as a sinusoidal function of time to simulate the bearings operating under cyclic loads. The closed form expressions for the bearing characteristics are obtained for the short porous journal bearings. It is observed that the negatively skewed surface roughness and couple stresses improve the performance of the porous journal bearings as compared to the smooth journal bearings with Newtonian lubricants. However, the presence of positively skewed surface roughness on the bearing surface affects its performance.     

Lubrication performance of finite journal bearings considering effects of couple stresses and surface roughness

To inspect the performance characteristics of finite journal-bearing systems, the combined effects of couple stress due to a Newtonian lubricant blended with additives and the presence of roughness on journal-bearing surfaces are studied in this article. Basing on the Stokes theory and Christensen’s stochastic model, the stochastic generalized Reynolds equation is deduced. The film pressure distribution equation is numerically solved by using the conjugate gradient method of iterations. According to the results, the couple stress effects can raise the film pressure of the lubricant fluid, improve the load-carrying capacity and reduce the friction parameter, especially at high eccentricity ratio. The surface roughness effect is dominant in long bearing approximation and the influence of transverse or longitudinal roughness to the journal bearing is in reverse trend. In general, the critical value of length-to-diameter is 1.1.     

Surface roughness effects in porous inclined stepped composite bearings lubricated with micropolar fluid

In this paper, the effect of surface roughness on the performance characteristic of porous inclined stepped composite bearings is studied. A generalised form of surface roughness is mathematically modelled by a stochastic random variable with non‐zero mean, variance and skewness. The generalised average Reynolds‐type equation is derived for the rough porous inclined stepped composite bearings with micropolar fluid. The closed‐form expressions are obtained for the fluid film pressure, load‐carrying capacity and frictional force. The results are presented for three different types of bearing system. The numerical computations of the results show that the negatively skewed surface roughness pattern increases fluid film pressure and load‐carrying capacity and decreases the coefficient of friction, whereas adverse effects were found for the positively skewed surface roughness pattern. Further, the rough porous inclined stepped composite bearing provides the largest load‐carrying capacity and the least coefficient of friction as compared with the porous plane slider and porous composite tapered concave bearings. Copyright © 2012 John Wiley & Sons, Ltd.     

计入轴瓦弹性的应力偶流体润滑分析

推导了计入轴瓦弹性的应力偶流体润滑轴承的变形雷诺方程。数值分析表明,刚性轴瓦的最大油膜压力值比弹性轴瓦的最大油膜压力值大,且随着应力偶参数的增大,最大油膜压力提高明显;润滑油分别为牛顿流体和应力偶流体时,弹性系数越大轴承的承载力越小,应力偶参数越大轴承的承载力越大,且轴承的偏心率越大,应力偶参数对承载力的影响越明显,应力偶参数对刚性轴瓦材料的影响比对弹性轴瓦材料的影响大。     

Film Shape Optimization for Two-Dimensional Rough Slider Bearings

A 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.     

Optimum load capacity of a slider bearing lubricated by a fluid with couple stress

The slider profile which gives the maximum load capacity of a slider bearing lubricated by an incompressible fluid with couple stress is considered. The optimum profile is a step function with riser location and step height ratio depending on the couple stress parameter. The results reduce to those of the classical Rayleigh problem when the couple stress parameter tends to zero. The optimum load capacity increases with the couple stress parameter.     

Refined simulation of friction power loss in crank shaft slider bearings considering wear in the mixed lubrication regime

Friction reduction is a fundamental factor in decreasing fuel consumption of internal combustion engines. During the design stage of the engine the simulation of friction in the crank mechanism plays a vital role to develop optimum solutions. Due to the interaction of oil and elastic structures with rough surfaces in slider bearings, complex simulation models have to be used for representing the relevant physical behavior. The following article is focused on crank shaft slider bearings of large engines.The article describes a procedure evaluated by measurements showing how to model wear profiles of slider bearings to reach a high quality friction forecast. A fundamental influencing factor of bearing friction is given by the mixed lubrication regime and it is considered in the simulation model as part of asperity contact friction and hydrodynamic friction. Further effects result from the compliance in radial and width directions of the bearing structure and the wear of the bearing surface. Furthermore, the specific operating conditions of the slider bearing such as load, temperature, shaft speed and oil characteristics are essential and have to be taken into account.The objective of this investigation is to propose the wear profile of the bearing surface for the simulation model to be treated iteratively, where simulation results for the amount of mixed lubrication are successively assessed. For this purpose an iterative procedure is introduced and validated by measurements on a slider bearing test rig.The applied simulation method is based on elastic multi-body systems; the lubrication film contact is calculated based on Reynolds differential equation via the pressure balance calculated iteratively in the time domain. The model accounting for the mixed lubrication regime is based on the theory of Greenwood and Tripp.     

Effect of surface roughness on the hydrodynamic lubrication of porous step-slider bearings with couple stress fluids

This paper presents the theoretical study of the effect of surface roughness on the hydrodynamic lubrication of porous step-slider bearings. A more general form of surface roughness is mathematically modeled by a stochastic random variable with non-zero mean, variance and skewness. The generalized average Reynolds-type equation is derived for the rough porous step-slider bearing lubricated with Stokes couple stress fluid. The closed-form expressions for the mean load carrying capacity, frictional force and the coefficient of friction are obtained. The performance of the rough porous step-slider bearing is compared with a corresponding smooth porous step-slider bearing. The numerical computations of the results show that the negatively skewed surface roughness pattern increases the load carrying capacity and decreases the coefficient of friction whereas the adverse effects were found for the positively skewed surface roughness pattern.     

Effect of Surface Roughness on Hydrodynamic Lubrication of Slider Bearings

The effect of surface roughness on the performance of hydrodynamic slider bearings is studied. A generalized form of surface roughness characterized by a stochastic random variable with non-zero mean, variance and skewness is assumed to define the bearing surface topography. Various film shapes such as: plane slider, exponential, secant and hyperbolic are considered. The results are obtained for the general lubricant film shape in integral form which are numerically computed for the shapes under consideration. The results are presented both graphically as well as in tabular form. The performance of a rough bearing can be considered in terms of an identical smooth bearing with an equivalent film thickness. It is observed, for the lubricant film shapes under consideration, that the increasing positive values of α, σ and ε decrease the load carrying capacity, frictional force and temperature rise while it increases the coefficient of friction. Increasing positive values of α and ε shift the center of pressure towards the outlet edge. For negative values of α, the increasing value reverses the trend of the effect on performance characteristics which is in conformity with the physical aspects of the problem. A similar trend is observed in case of the effect of negative values of ε. Thus, a negatively skewed surface roughness modifies the performance of the slider bearings whereas the performance of a bearing suffers on account of positively skewed surface roughness. Moreover, it is noticed that in the case of exponential and hyperbolic slider bearings the effect of increasing values of σ is more pronounced whereas in case of plane slider and secant shaped slider this effect is marginal.