Static characteristics of ferrofluid finite journal bearing considering rotational viscosity effect

Considering the rotation of ferromagnetic particles, the present study investigates hydrodynamic lubrication by ferrofluids of finite journal bearings using the Shliomis model. A magnetic field created by displaced finite wire is used. A numerical solution for the modified Reynolds equation using the finite difference method is obtained. Static characteristics of finite journal bearings are analysed using three control parameters: rotational viscosity, magnetization and volume concentration of the ferromagnetic particles. It is shown that the pressure, load capacity, attitude angle and side leakage increase and the friction coefficient decreases when increasing the value of each control parameter. Similar trends are also obtained when increasing values of eccentricity for a fixed value of each control parameter except for the decrease of the attitude angle. Copyright © 2016 John Wiley & Sons, Ltd.     

Ferrofluid squeeze film in a long journal bearing

A theoretical study and comparison were made of squeeze film behaviour in an infinitely long journal bearing using the ferrofluid flow models of Neuringer–Rosensweig, Jenkins and Shliomis with uniform and non-uniform magnetic fields. Expressions were obtained for the pressure, load capacity and response time of the squeeze film using the flow models of Jenkins as well as Shliomis. The results corresponding to the Neuringer–Rosensweig model were deduced from the Jenkins model. Computed values of dimensionless load capacity and response time were displayed in tabular form. Their values increased with increasing values of the eccentricity ratio in all the three models. They decreased or increased according to whether the values increased were those of the Jenkins material constant or the rotational viscosity parameter of Shliomis. A uniform magnetic field could not produce magnetic pressure in the Neuringer–Rosensweig model, but it could affect the bearing characteristics in the Shliomis model owing to the rotational viscosity. The load capacity and squeeze time are more in the case of a non-uniform magnetic field than in the case of a uniform magnetic field.     

Calculated load capacity of non-newtonian lubricants in finite width journal bearings

Starting from the most general type of fluid flow equation connecting cubic shear stress to rate of shear for non-Newtonian lubricants, a modified form of Reynolds' equation was derived for steady finite width journal bearings. The finite difference technique with successive over relaxation was used incorporating Reynolds' boundary conditions for pressure to obtain the pressure distribution and hence the load capacity and the attitude angle. It is shown that the flatter pressure profile and higher load capacity at low eccentricity ratios have practical advantages. The apparent viscosity loss at higher rates of shear decreases the load capacity at higher eccentricity ratios but it is expected that the flatter viscosity temperature slope of the polymer thickened non-Newtonian lubricants will compensate for their apparent viscosity decrease.     

Steady-state thermo-hydrodynamic analysis of cylindrical fluid film journal bearing with an axial groove

A steady-state thermohydrodynamic analysis of an axial groove journal bearings in which oil is supplied at constant pressure is performed theoretically. Thermohydrodynamic analysis requires simultaneous solution of Reynolds equation, energy equation and heat conduction equations in the bush and the shaft. From parametric study it is found that the temperature of the fluid film raises due to frictional heat thereby viscosity, load capacity decreases. Increased shaft speed resulted in increased load carrying capacity, bush temperature, flow rate and friction variable. It is difficult to obtain the solution due to numerical instability when the bearing is operated at high eccentricity ratios.     

Surface roughness effect on finite journal bearings with flexible porous liners

The effects of surface roughness on the static characteristics of finite porous journal bearings under hydrodynamic lubrication conditions are investigated in this paper. The well‐established Christensen stochastic theory of hydrodynamic lubrication of rough surfaces is used to incorporate the effects of surface roughness into the Reynolds equation. The analysis takes into account the flexibility of the porous liner by using a thin liner model. The effects of velocity slip at the surface of the porous medium are considered in the analysis by using the Beavers‐Joseph criterion. The mathematical model is then solved numerically by finite‐difference methods for mean hydrodynamic pressure, which in turn gives the hydrodynamic load. The effects of the surface roughness parameter, surface pattern, eccentricity ratio, length‐to‐diameter ratio, permeability parameter, and flexibility parameter on the hydrodynamic load‐carrying capacity, attitude angle, and friction factor are discussed.     

Different Magnetic Models in the Design of Hydrodynamic Journal Bearings Lubricated with Non-Newtonian Ferrofluid

This work is concerned with theoretical study of hydrodynamic journal bearings lubricated with ferrofluids exhibiting non-Newtonian behavior. Based on the momentum and continuity equations for ferrofluid under an applied magnetic field, a modified Reynolds equation has been obtained. Assuming linear behavior for the magnetic material of the ferrofluid, the magnetic force was calculated. The Reynolds equation has been derived to be able to apply to any magnetic field distribution model. Using different magnetic field models, the equation has been solved numerically by the finite-difference technique with appropriate iterative technique and pressure distributions have been obtained. The boundary shape of the load-carrying active regions (positive-pressure regions) and cavitation regions (zero-pressure regions) could be then determined. The solution renders the bearing performance characteristics, namely: load-carrying capacity, attitude angle of the journal center, frictional force at the journal surface, friction coefficient and bearing side leakage. The results indicated that the flow-behavior index has a large effect on the bearing performance. When the bearing operates at high eccentricity ratios, the increase of flow-behavior index gives higher load capacity, lower attitude angle, higher frictional force, lower friction coefficient and higher side leakage. At low eccentricity ratios where the magnetic effects are significant, the effect of the flow-behavior index depends mainly on the magnetic field distribution model used.     

THD Effects of Static Performance Characteristics of Infinitely Wide Turbulent Journal Bearings

Formulas for static parameters were found for infinitely wide turbulent full journal bearings that correlate either load capacity or friction coefficient for thermohydrodynamics (THD) effects in terms of a single THD parameter. The database was built by numerical simulation of turbulent liquid lubricant flows with various eccentricity ratios in a wide range of the Reynolds number for both isoviscous and THD cases. The least-squares method was applied to the groups of parameters yielding the formulas of load capacity, friction coefficient, and attitude angle. The isoviscous attitude angle was fitted as a function of the maximum-to-minimum film thickness ratio, and the variation of attitude angle due to THD is linearly dependent on the THD-to-isoviscous load capacity ratio. With the formulas provided in this study, designers can quickly determine static parameters of turbulent journal bearings without the burden of labor-intensive numerical computation of the governing differential equations.     

以超临界二氧化碳为介质的径向箔片轴承静特性分析

以超临界二氧化碳(S-CO2)布雷顿循环所用压缩机中的径向箔片气体轴承为研究对象,考虑S-CO2在近临界区的实际物性,运用有限差分法数值求解变密度变黏度湍流雷诺方程,耦合弹性箔片变形方程,计算以S-CO2为润滑介质的径向气体轴承的气膜压力分布规律,并分析近临界区S-CO2物性变化对轴承承载力、摩擦力矩的影响.计算结果表...     

Hydrodynamic lubrication of porous journal bearings using a modified Brinkman-extended Darcy model

A numerical solution for the hydrodynamic lubrication of finite porous journal bearings considering the flexibility of the liner is introduced. The Brinkman-extended Darcy equations and the Stokes' equations are utilized to model the flow in the porous region and fluid film region, respectively. A stress jump boundary condition at the porous media/fluid film interface and effects of viscous shear are included into the lubrication analysis. Elrod's cavitation algorithm, which automatically predicts film rupture and reformation in the bearing, is implemented in the solution scheme. The present analysis predictions for pressure distributions, load carrying capacity, and friction factor are in good agreement with three different sets of experimental results available in the literature. Furthermore, the effects of dimensionless permeability parameter, and stress jump parameter on performance parameters such as load carrying capacity, side leakage, friction factor, and attitude angle, are presented and discussed.     

轴表面DLC涂层对滑动轴承润滑承载性能的影响*

为研究轴表面类金刚石(DLC)涂层对滑动轴承承载性能的影响,利用滑动轴承实验台测试轴线对中及倾斜工况下灰铸铁、铝合金和聚酰亚胺(PI)涂层轴承分别与40Cr钢轴和DLC涂层轴配合时的轴心轨迹和极限载荷,并测试3种材料与40Cr钢和DLC涂层的摩擦因数。结果表明:相较与40Cr钢配合,灰铸铁和铝合金与DLC涂层配合时摩擦因数减小,重载下轴承偏心率减小,轴线对中工况下灰铸铁轴承的极限载荷超过10 MPa,铝合金轴承的极限载荷增大到7.8 MPa(增大1.1倍),轴线倾斜工况下轴承抱死失效时边缘变形增大;但重载下PI涂层与DLC涂层配合时摩擦因数增大,轴线对中工况下轴承极限载荷减小至3.6 MPa(减小44%),轴线倾斜工况下轴承抱死失效时边缘变形减小。     

Approximate Solution of Oil Film Load-carrying Capacity of Turbulent Journal Bearing with Couple Stress Flow

The instability of the rotor dynamic system supported by oil journal bearing is encountered frequently, such as the half-speed whirl of the rotor, which is caused by oil film lubricant with nonlinearity. Currently, more attention is paid to the physical characteristics of oil film due to an oil-lubricated journal bearing being the important supporting component of the bearing-rotor systems and its nonlinear nature. In order to analyze the lubrication characteristics of journal bearings efficiently and save computational efforts, an approximate solution of nonlinear oil film forces of a finite length turbulent journal bearing with couple stress flow is proposed based on Sommerfeld and Ocvirk numbers. Reynolds equation in lubrication of a finite length turbulent journal bearing is solved based on multi-parametric principle. Load-carrying capacity of nonlinear oil film is obtained, and the results obtained by different methods are compared. The validation of the proposed method is verified, meanwhile, the relationships of load-carrying capacity versus eccentricity ratio and width-to-diameter ratio under turbulent and couple stress working conditions are analyzed. The numerical results show that both couple stress flow and eccentricity ratio have obvious influence on oil film pressure distribution, and the proposed method approximates the load-carrying capacity of turbulent journal bearings efficiently with various width-to-diameter ratios. This research proposes an approximate solution of oil film load-carrying capacity of turbulent journal bearings with different width-to-diameter ratios, which are suitable for high eccentricity ratios and heavy loads.     

多孔质气体静压径向轴承倾斜状态特性研究

为研究倾斜状态对多孔质气体静压轴承性能的影响,基于一维流动模型应用有限元方法对多孔质气体静压轴承进行数值分析,研究渗透率、初始偏心距、倾斜角度等重要因素对多孔质径向轴承承载能力和弯矩的影响。结果显示:轴承初始偏心距对轴承承载能力影响很大;在相同初始偏心距时,倾斜状态下的径向轴承承载能力随着轴承倾角的增大而增大;在相同倾斜角度时,径向轴承承载能力分别随着轴承初始偏心距和轴承渗透率的增大而增大,并且初始偏心距越大,渗透率对承载能力的影响越大。     

Investigations on the Influence of Surface Texturing on a Couple Stress Fluid–Based Journal Bearing by Using JFO Boundary Conditions

The present study was conducted to examine the effect of laser surface texturing combined with couple stress fluids on the hydrodynamic lubrication of finite journal bearing in this work. The Jakobsson-Floberg-Olsson (JFO) boundary conditions were engaged instead of Reynolds boundary conditions to achieve realistic results. Moreover, the results were computed and authenticated with the previous published work. It was observed that the load-carrying capacity is increased with couple stresses for smooth journal bearings at different eccentricity ratios. However, the increment in load-carrying capacity with texture affects only at low eccentricity ratios. The combined effects of texturing with couple stress fluids lower the performance of journal bearings at different eccentricity ratios.     

弹性箔片动压径向气体轴承起飞转速和承载能力的实验研究

在建立的气体轴承性能测试实验台上对新型弹性箔片气体动压径向轴承进行了起飞转速和承载能力的实验研究,并分别通过摩擦力矩和径向位移响应频谱两种方法分析了轴承的起飞转速。结果表明:轴承起飞后摩擦力矩逐渐减小并趋于稳定,且径向位移响应频谱图上只有较大的低倍频分量出现,高倍频分量和其它频率分量要小得多;两种分析方法得到的轴承起飞转速基本吻合;载荷越大,轴承和转子中心的偏心距越大;由于箔片弹性变形使卸载过程存在能量损失,同样载荷下卸载时的偏心距比加载时大。     

Thermo-hydrodynamic analysis of herringbone grooved journal bearings

Steady-state and stability characteristics of herringbone grooved journal bearings (HGJBs) are found considering thermal effect. The temperature of the fluid film rises significantly due to the frictional heat, thereby the viscosity of the fluid and the load carrying capacity decrease. A thermodynamic analysis requires the simultaneous solution of Reynolds equation along with energy equation of the fluid and heat conduction equations in the bush and the shaft. The linearized first-order perturbation technique is employed for the prediction of stiffness and damping coefficients of the oil film. Thereafter mass parameter and whirl ratio are found from the stability analysis. It is difficult to obtain the solution due to the numerical instability when the bearing is operated at high eccentricity ratios.     

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.     

Hydrodynamic lubrication of finite porous journal bearings—Use of the Brinkman-extended Darcy model

This paper applies the Brinkman-extended Darcy model (BEDM) to investigate the hydrodynamic lubrication of finite porous journal bearings. A finite difference technique employing the Preconditioned Conjugate Gradient method (PCGM) of iteration is used to solve the modified Reynolds equation. The results show that the influences of viscous shear stresses on the lubrication performance of porous journal-bearing systems are apparent and not negligible. Comparing with those of the Darcy model (DM), the effects of viscous shear stresses of the BEDM provide an increase in the load capacity, as well as a reduction in the friction parameter; and the quantitative effects of the viscous shear stresses on the static characteristics are more pronounced for the cases of large length-to-diameter ratios.     

Texture shape effects on hydrodynamic journal bearing performances using mass-conserving numerical approach

ABSTRACT

It is a known fact that incorporating textures in the contact surfaces can significantly enhance bearing performances. The purpose of this paper is to outline the effects of texture bottom profiles and contour geometries on the performances of hydrodynamic textured journal bearings. The analysis was conducted using computational approach to test eight texture shapes: rectangular, cylindrical, spherical, triangular (TR, T1, T2, T3) and chevron. The steady-state Reynolds equation for modelling the hydrodynamic behaviour of thin viscous film was solved using finite difference technique and mass conservation algorithm (JFO boundary conditions), taking into account the presence of textures on both full film and cavitation regions. The comparison with the benchmark data shows good consistency and an enhancement in bearing performances (load carrying capacity and friction). The results clearly show that the mechanisms of wedge effect and micro-step bearing for the full/partial texturing feature are the main crucial parameters, where the convergent wedge effect present in T2 triangular texture shape can significantly enhance the load-carrying capacity, while the divergent wedge action causes a net load loss. Considering the right arrangement of textures on the contact surface, their surface contours can have a significant impact on the performance of hydrodynamic journal bearings at high eccentricity ratios.     

多叶动压气体滑动轴承静态特性的有限差分算法

多叶动压气体滑动轴承因其结构简单、摩擦阻力低、旋转精度高和无环境污染等优点,在高速离心分离机、空气压缩机和透平膨胀机等旋转机械中应用广泛。为探究多叶动压气体滑动轴承的静态性能,通过数学变换将三叶动压轴承的气体润滑Reynolds方程转化为标准偏微分方程形式,利用有限差分法和超松弛迭代法进行数值求解,研究气膜厚度和气膜压力分布、承载力、摩擦因数和质量流量等静态性能,随偏心率、预负荷系数、轴承数、长径比及瓦块分布位置的变化规律。结果表明：三叶轴承的承载力和轴颈表面摩擦因数随偏心率和长径比的增加而增加,而偏位角和质量流量随偏心率和预负荷系数的增加则呈现出相反的变化趋势;随着轴承数和预负荷系数的增大,承载力和摩擦因数显著提高,偏位角和质量流量则逐渐减小;瓦块分布位置对三叶动压气体滑动轴承的静态性能影响显著,其中瓦上承载方式的承载力、偏位角和质量流量明显高于瓦间承载方式。     

Numerical Calculation of Rotation Effects on Hybrid Air Journal Bearings

Hybrid air journal bearings are of great importance in the precision engineering. Despite much progress, the influence of the aerostatic effect and the aerodynamic effect on the bearings is still not clear. Numerical calculation is a useful technique to evaluate bearing performance. Many theoretical problems related to Reynolds equation have been figured out by numerical simulation. The present study analyzes the effects of rotational speed—that is, the bearing speed number—on the performance of hybrid bearings. The behaviors of the pure aerostatic bearing and the pure aerodynamic bearing are investigated for comparison. The second-order finite difference method (FDM) and an iterative procedure are proposed to solve the Reynolds equation and derive the air film pressure distribution. The bearing characteristics such as load capacity, stiffness, friction coefficient, attitude angle, and mass inflow rate are taken into consideration. The research reveals the very dependence of the hybrid bearing's performance on the journal rotation and eccentricity ratio. The numerical results indicate that at a small bearing speed number of 0.223 and eccentricity ratio of 0.15, about 99.8% of the load capacity and 99.7% of the stiffness are determined by the aerostatic effect, whereas at a large bearing speed number of 2.229 and eccentricity ratio of 0.55, about 63.2% of the load capacity and 83.3% of the stiffness are determined by the aerodynamic effect.