Analysis of squeeze film performance between rough porous infinitely long parallel plates with porous matrix of non-uniform thickness under presence of magnetic fluid lubricant

Abstract

The performance of a magnetic fluid based squeeze film between infinitely long porous rough parallel plates with porous matrix of non-uniform thickness has been investigated. The bearing surfaces are considered to be transversely rough. The stochastic film thickness characterising the random roughness is assumed to be asymmetric with non-zero mean and variance. A magnetic fluid is used as a lubricant and the external magnetic field is oblique to the lower plate. With usual assumptions of hydrodynamic lubrication the associated Reynolds' equation is solved with suitable boundary conditions. Then expressions for pressure distribution, load carrying capacity and response time are obtained. It is observed that the load carrying capacity increases nominally due to magnetic fluid lubricant resulting in improved performance. But it is also seen that the composite roughness of the bearing surfaces introduces an adverse effect which gets more compounded due to the thickness ratio. However, the negative effect can be compensated to certain extent by the magnetic fluid lubricant in the case of negatively skewed roughness. This compensation further enhances when negative variance is involved. This study tends to suggest that the thickness ratio may play a crucial role for a better performance of the magnetic fluid based bearing system besides providing an additional degree of freedom.     

Combined effects of surface roughness and viscosity variation due to additives on long journal bearing

Abstract

The combined effects of surface roughness and viscosity variation due to additives on long journal bearing are analytically studied. The variation in viscosity along the film thickness is considered. The presence of solid particles in the lubricant is an increased effective viscosity, which increases the load carrying capacity and decreases the frictional coefficient, whereas the viscosity variation tends to decrease both the load carrying capacity and coefficient of friction for non-micropolar fluid case. The modified Reynolds type equation for surface roughness has been derived on the basis of Eringen’s micropolar fluid theory. The generalised stochastic random variable with non-zero mean, variance and skewness is assumed to mathematically model the surface roughness on the bearing surface. Numerical results were obtained for the fluid film pressure, load carrying capacity and the coefficient of friction. It is observed that the combined effect is to increase the load carrying capacity and to decrease the coefficient of friction, which improves the performance of the bearing.     

复合材料水润滑艉轴承结构设计研究

基于ANSYS CFX流固耦合数值计算方法,对水润滑复合材料艉轴承的润滑性能及结构设计开展研究,阐述了不同水槽结构、间隙比、长径比、直径等对轴承承载力以及水膜压力、轴承变形量、最小水膜厚度、轴承摩擦因数的影响规律。并利用水润滑轴承试验台研究了不同水槽结构对轴承启动摩擦转矩、转变速度以及摩擦因数的影响。研究表明,轴承摩擦因数、水膜最大压强、轴承最大变形随水槽数增多而增大;轴承承载力、最小水膜厚度随间隙比增大而减小,随长径比增大而增大。总结了直径为100~500 mm、长径比为2~3、间隙比为0.1%~0.2%的水润滑艉轴承承载力的变化规律,为水润滑艉轴承设计提供一定的理论依据。     

A study on the performance of a magnetic fluid based squeeze film in curved porous rotating rough annular plates and deformation effect

Efforts have been made to analyze the behaviour of a magnetic fluid based squeeze film between rotating transversely rough porous annular plates incorporating elastic deformation. The results suggest that the roughness of the bearing surfaces affects the performance adversely although; the bearing registers an improved performance owing to the magnetic fluid lubricant. It is seen that the deformation causes reduced load carrying capacity. This investigation reveals that the negative effect of porosity, deformation and standard deviation can be minimized up to certain extent by the positive effect of the magnetic fluid lubricant in the case of negatively skewed roughness.     

Effects of operating conditions and supply hole diameter on the performance of a rectangular aerostatic bearing

The present study is an experimental investigation of the performance characteristics of an externally pressurized rectangular recessed gas bearing operating under different working conditions. It includes the measurements of pressure, load carrying capacity, and mass flow rate. The experiments covered a wide range of film thicknesses and supply pressures. In addition, pads of different supply hole diameters were used. The results obtained from the present investigation show that the effect of varying the supply hole diameter on bearing performance is significant. Increasing the supply hole diameter to bearing length ratio has the effect of increasing the recess pressure and load carrying capacity. Further, as the supply pressure and/or film thickness increases the dimensionless load carrying capacity decreases and the lubricant mass flow rate increases.     

Porous inclined stepped composite bearings with micropolar fluid

Abstract

This paper describes the theoretical analysis of the effect of micropolar fluid on the lubrication characteristics of porous inclined stepped composite bearing. The lubricant with additives in the film region and also in the porous region is modelled as Eringen's micropolar fluid, which is characterised by the presence of suspended rigid particles with microstructures. The generalised Reynolds type equation is derived for the most general porous bearing configuration (porous composite bearings) lubricated with micropolar fluid. The closed form expressions are obtained for the fluid film pressure, load carrying capacity, frictional force and coefficient of friction. These expressions can be utilised to obtain the performance characteristics of four different bearing systems, namely, porous plane inclined slider, porous composite tapered land bearing, porous stepped bearing and composite porous tapered concave bearing. It is observed that the micropolar fluid lubricants provide an increased load carrying capacity and decreased coefficient of friction as compared to the corresponding Newtonian case.     

浮环弹性变形对浮环动静压轴承润滑特性的影响

浮环轴承在高速工况下运行时,浮环表面在油膜压力作用下会发生弹性变形,影响轴承润滑性能。针对带有深浅腔的浮环动静压轴承,采用有限元法和有限差分法耦合求解油膜Reynolds方程、能量方程和温黏关系式,采用变形矩阵法求解弹性变形方程,计算浮环弹性变形分布;在浮环平衡的基础上,分析浮环变形对环速比、油膜承载力、端泄流量等润滑特性参数的影响。结果表明：浮环弹性变形分布与油膜压力分布呈现一致性,转速越高,偏心越大,变形越明显;考虑浮环弹性变形,浮环达到平衡状态时,内膜偏心率增加,环速比减小,轴承承载力与摩擦力矩均有所增加;由于浮环变形对内、外膜间隙及流动液阻的不同影响,使得内膜端泄流量增加,外膜端泄流量减少。     

Effect of viscosity variation due to lubricant additives in journal bearings

Micropolar fluid theory, which is a possible non-newtonian model of a suspension of rigid particle additives, is applied to the study of the lubrication of an infinitely long and an infinitesimally short journal bearing. The variation in viscosity along the film thickness is taken into consideration. The prominent feature of the presence of solid particles in the lubricant is an increased effective viscosity which increases the load capacity and decreases the coefficient of friction. Whereas viscosity variation tends to decrease both the load and the coefficient of friction for the non-micropolar case, the combined effect is to increase the load and to decrease the coefficient of friction.     

考虑稀薄气体有效黏度的微轴承弹流润滑研究

气体稀薄效应和轴瓦弹性变形对微流体设备中气体微型轴承润滑特性影响显著.根据Veijola提出的稀薄气体有效黏度模型,采用有限元法建立柔度矩阵计算轴瓦表面弹性变形量,并推导考虑有效黏度与弹性变形影响的修正Reynolds方程.通过联立求解超薄气膜润滑修正Reynolds方程、稀薄气体有效黏度方程和三维轴瓦弹性方程,分析轴...     

A study of optimum load capacity of slider bearings lubricated with power law fluids

A general theoretical study of an infinitely wide lubricated slider bearing is presented, considering the lubricant to be an incompressible, isothermal, power law fluid. A set of algebraic equations is developed to obtain the pressure gradient for any value of the power law index. To illustrate the mathematical development, the set of equations is used to calculate the pressure gradient for two special forms of slider bearings, viz., inclined and parabolic slider bearings. In these two cases, the variation of pressure, load capacity, coefficient of friction, etc. for a range of fluid- and bearing-parameters is presented. In order to obtain optimum load capacity for an inclined and a parabolic slider bearing, the variations of load capacity, coefficient of friction, etc., with respect to the simultaneous changes of the inlet–oulet film height ratio and of the power law index of lubricants are also analysed. The results are presented both numerically and graphically. The results reveal that in the cases of an inclined and a parabolic slider bearings the inlet–outlet film height ratio for the optimum load capacity depends on the power law index of lubricants. Further, for each value of power law index, there exists a value of inlet–outlet film height ratio for which the frictional coefficient is minimum.     

LOADING CAPACITY ANALYSIS OF THE MISALIGNED CONICAL-CYLINDRICAL BEARING WITH NON NEWTONIAN LUBRICANTS

A novel numerical method to lubricate a conventional finite diameter conical-cylindrical bearing with a non-Newtonian lubricant, while adhering to the power-law model, is presented. The elastic deformation of bearing and varied viscosity of lubrication due to the pressure distribution of film thickness are also considered. Simulation results indicate that the normal load carrying capacity is more pronounced for higher values of flow behavior index n, higher eccentricity ratios and larger misalignment factors. It is found that the viscosity-pressure to the effect of lubricant viscosity is significant.     

Effects of lubricant additives on the performance of hydrodynamically lubricated journal bearings

A non-Newtonian rheological model to investigate theoretically the effects of lubricant additives on the steady state performance of hydrodynamically lubricated finite journal bearings is introduced. In this model, the non-Newtonian behavior resulting from blending the lubricant with polymer additives is simulated by Stokes couple stress fluid model. The formed boundary layer at the bearing surface is described through the use of a hypothetical porous medium layer that adheres to the bearing surface. The Brinkman-extended Darcy equations are utilized to model the flow in the porous region. A stress jump boundary condition is applied at the porous media/fluid film interface. A modified form of the Reynolds equation is derived and solved numerically using a finite difference scheme. The effects of bearing geometry, and non-Newtonian behavior of the lubricant on the steady-state performance characteristics such as pressure distribution, load carrying capacity, side leakage flow, and coefficient of friction are presented and discussed. The results showed that lubricant additives significantly increase the load carrying capacity and reduce both the coefficient of friction and the side leakage as compared to the Newtonian lubricants.     

UHMWPE复合材料水润滑轴承润滑状态转变性能研究

水润滑轴承润滑介质的黏度较低,轴承动压润滑难以形成。研究水润滑轴承润滑状态转变特性,可为水润滑复合材料轴承的设计和优化提供依据。建立水润滑轴承流固耦合计算模型,研究轴承承载力、水膜压力、轴承变形量随工况的变化关系,提出水膜厚度测试方法,研究轴承摩擦因数、水膜厚度随转速、负载的变化规律。研究结果表明:随偏心率和转速增大,轴承承载力、最大水膜压力和最大变形量均逐渐增大;随转速增大,轴承承载力、最大水膜压力和最大变形量的增幅逐渐减小。试验发现随着负载增大,改性UHMWPE轴承从混合润滑向动压润滑转变的膜厚比逐渐减小。     

Performance characteristics for the hydrostatic thrust bearing of a saw blade

A semi-analytical solution is presented to obtain the pressure distribution, the load capacity, the frictional moment and the lubricant flow rate for a laminar flow, hydrostatic bearing with its axis offset from thee axis of the saw blade. The general equations are developed and solved for a variable film thickness due to plate vibrations. It was found that the load, friction and lubricant flow rate are strong functions of film thickness variations , bearing number λ and the bearing offset from the rotation axis     

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.     

Lubricant additives effects on the hydrodynamic lubrication of misaligned conical–cylindrical bearings

Conical–cylindrical bearings are used in electrohydraulic servo systems to improve the control accuracy, eliminate the static friction and increase the normal load‐carrying capacity. A non‐Newtonian rheological model to investigate theoretically the effects of lubricant additives on the performance of misaligned conical–cylindrical bearings is proposed in this study. In this model, the non‐Newtonian behaviour resulting from blending the lubricant with polymer additives is simulated by Stokes couple stress fluid model. The formed boundary layer at the bearing surface is described through the use of a hypothetical porous medium layer that adheres to the bearing surface. The Brinkman‐extended Darcy equations are utilised to model the flow in the porous region. A stress jump boundary condition is applied at the porous media/fluid film interface. The misalignment of the cylinder rod is also considered. A modified form of the Reynolds equation is derived and solved numerically using a finite difference scheme. The effects of bearing geometry and non‐Newtonian behaviour of the lubricant on the steady‐state performance characteristics such as pressure distribution, load‐carrying capacity and coefficient of friction are presented and discussed. The results showed that lubricant additives significantly increase the load‐carrying capacity and reduce the coefficient of friction as compared to the Newtonian lubricants. Furthermore, the misalignment of the piston rod has significant effects on the performance of conical–cylindrical bearings. Copyright © 2007 John Wiley & Sons, Ltd.     

UHMWPE基水润滑尾轴承润滑特性仿真及试验研究

针对UHMWPE基高分子复合材料水润滑轴承的润滑特性开展研究。采用双向流固耦合算法研究弹性模量和泊松比等材料参数以及转速、负载等工况参数对水润滑轴承偏心率、最大水膜压力、轴承最大变形量、最小水膜厚度、摩擦因数等润滑特性的影响。基于改性UHMWPE高分子复合材料轴承的试验,验证了仿真方法的正确性。研究表明:计入弹性变形的流固耦合算法在研究高分子复合材料轴承性能方面具有更高的精度;随轴瓦材料弹性模量和泊松比的增大,轴承承载力逐渐增大、弹性变形量逐渐减小;随负载增大,轴承最大水膜压力和最大变形量基本呈线性增长;随转速增大,轴承最大水膜压力和轴承最大变形量显著减小;对于高分子复合材料轴承,低速、重载工况下不计入弹性变形的算法误差更大。     

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.     

热流固耦合下柱塞泵配流副参数对摩擦性能的影响

为探讨热流固耦合下柱塞泵配流副参数对摩擦性能的影响,建立配流副的润滑模型,采用有限差分法对雷诺方程、能量方程和弹性变形方程进行求解,考虑黏度-温度、黏度-压力的关系,利用松弛迭代法求得热流固耦合下油膜压力、弹性变形与油膜温度分布的数值解,并运用MATLAB得到油膜压力、弹性变形、油膜温度分布云图;分析配流副参数对油膜承载力、摩擦力、摩擦转矩和摩擦因数的影响。结果表明：缸体倾斜角度和初始油膜厚度对油膜承载力的影响较大,增大缸体倾斜角度和减小初始油膜厚度,可提高油膜承载能力;减小润滑油黏度、增大初始油膜厚度能有效降低润滑摩擦过程中的摩擦力和摩擦因数。     

基于流固耦合的波箔动压气体轴承承载性能优化

基于有限元软件Ansys Workbench,建立波箔动压气体轴承在可压缩流体介质中运动的有限元模型,采用6DOF动网格计算方法对轴承的运动状态进行流固耦合数值模拟,探讨不同转速和波箔片结构参数（波箔的长度比、高度以及厚度）对轴承承载性能的影响规律。结果表明：轴承气膜压力大小的分布与平箔片变形量的大小成对应关系,说明提出的流固耦合方法能很好地反映波箔动压气体轴承的润滑状态;随着转速的增大,轴承动压效应不断增强,承载力增大,且平箔片的结构变形不断增大,致使气膜压力的收敛区发生波动;随着波箔的长度比和波箔片厚度的增加,轴承承载力先快速增大后趋于稳定,而波箔片高度对承载力影响不大,表明适当增加波箔的长度比和波箔片厚度可以提高承载力。