Squeeze film characteristics of conical bearings with combined effects of piezo-viscous dependency and non-Newtonian couple stresses

In this paper, the analysis of squeeze film characteristics of conical bearings with combined effects of piezo-viscous dependency and couple stress fluid is presented. On the basis of the Stokes microcontinuum theory of couple stress fluid model and Barus experimental research, a modified Reynolds equation is derived, the standard perturbation technique is used to solve the highly non-linear Reynolds equation and approximate analytical solution is obtained for the squeeze film pressure, load carrying capacity and squeeze film time. According to the results obtained, the effect of viscosity pressure dependency on the squeeze film lubrication of conical bearings with couple stress fluids is to improve the load carrying capacity significantly and lengthen the squeeze film time as compared to iso-viscous Newtonian case.     

Elastohydrodynamic Lubrication of Rough Surfaces under Oscillatory Line Contact with Non-Newtonian Lubricant

This paper presents the results of a transient analysis of elastohydrodynamic lubrication (EHL) of two parallel cylinders in line contact with a non-Newtonian lubricant under oscillatory motion. Effects of the transverse harmonic surface roughness are also investigated in the numerical simulation. The time-dependent Reynolds equation uses a power law model for viscosity. The simultaneous system of modified Reynolds equation and elasticity equation with initial conditions was solved using the multigrid, multilevel method with full approximation technique. The film thickness and the pressure profiles were determined for smooth and rough surfaces in the oscillatory EHL conjunctions, and the film thickness predictions were verified experimentally.

For an increase in the applied load on the cylinders or a decrease in the lubricant viscosity, there is a reduction in the minimum film thickness, as expected. The predicted film thickness for smooth surfaces is slightly higher than the film thickness obtained experimentally, owing primarily to cavitation that occurred in the experiments. The lubricant film under oscillatory motion becomes very thin near the ends of the contact when the velocity goes to zero as the motion direction changes, but a squeeze film effect keeps the fluid film thickness from decreasing to zero. This is especially true for surfaces of low elastic modulus. Harmonic surface roughness and the viscosity and power law index of the non-Newtonian lubricant all have significant effects on the film thickness and pressure profile between the cylinders under oscillatory motion.     

Effect of Piezoviscous Dependency and Couple Stress on Squeeze Film Lubrication Between Parallel Stepped Plates

Theoretical analysis of the effect of piezoviscous dependency and couple stress on squeeze film lubrication between parallel stepped plates is presented in this article. According to the Stokes microcontinuum theory of couple stress fluids, the modified Reynolds equation is derived by considering viscosity variation along the film thickness. The standard perturbation technique is used to solve the nonlinear Reynolds equation and an approximate analytical solution for the film pressure is obtained. It is found that the effect of couple stresses and pressure-dependent viscosity variation increases the load-carrying capacity and lengthens the squeeze film time.     

Inertia effect in squeeze film air contact

The analysis presented in this paper explores the effect of air inertia on the squeeze film air contact operation and assesses the contribution of air inertia to the mechanism of squeeze film formation. Derivation of the Reynolds equation containing inertia term for squeeze film air contact is outlined. An average inertia concept is used in dealing with inertia force across the squeeze film thickness. Numerical iteration is used in solving for the non-linear inertia term in the modified Reynolds equation. Results are compared with the performance of the squeeze film air contact without inertia.     

A numerical model of an oscillating squeeze film between a rubber surface and a rigid surface

A numerical model for the hydrodynamic behavior of an oscillating squeeze film between a rubber surface and a rigid surface is presented. The effects of roughness of the rubber surface on the hydrodynamic force and the leakage flow rate in the squeeze film are analyzed. A modified Reynolds equation, Laplace equation and a three-parameter viscoelastic constitutive equation are solved simultaneously to obtain the pressure distribution in the squeeze film and the deformation of the rubber surface. Equations are discretized into finite difference equations and solved by Gauss-Siedel iteration method. It is found that increasing roughness of the surface profile significantly increases the hydrodynamic force accompanied by a small decrease in the leakage flow rate. Spatial distribution of the roughness of the rubber surface has no significant effect on the leakage flow rate or hydrodynamic force. The results obtained from the presented simple model are compared with the experimental results available in the literature and a very good agreement is found.     

圆弧齿轮热弹性流体动力润滑数值解

根据圆弧齿轮啮合点具有二维表面速度的点接触弹流模型,在变网格下联立求解能量方程、雷诺方程和弹性位移方程等,获得了齿面接触区内的温度、压力和润滑膜厚度分布。计算考虑了润滑剂粘度和密度随温度压力变化和挤压膜效应等因素。用恩瑞模型进行了齿面摩擦分析,讨论了工况变化对齿轮润滑性能的影响。结果表明：在中等载荷或转速时,圆弧齿轮的润滑膜厚度是渐开线齿轮的3倍以上,而齿面摩擦因数比渐开线齿轮小近一个量级;圆弧齿轮沿齿宽方向的滚动速度对润滑膜性态起主导作用,沿齿高方向的滑动速度对润滑膜温升及膜厚影响不大;齿面挤压膜效应对压力分布有一定影响。     

海水润滑赛龙轴承热弹流润滑理论分析

利用Reynolds方程,对海水润滑条件下赛龙轴承在考虑热效应时的弹流润滑问题进行数值模拟,讨论载荷、转速和轴承轴径大小对海水润滑膜压力及膜厚的影响。结果表明:热效应对于水膜压力影响很小,而考虑热效应时的膜厚会有所减小;随载荷的增大,压力峰值有所增大,膜厚随载荷的增大有明显的减小;随转速的增大压力峰值减小,而膜厚随转速的增大而有明显的增大;轴径的大小对于水膜压力和膜厚的大小影响不明显。     

Performance analysis of four-pad hydrostatic squeeze film dampers loaded between pads under laminar and turbulent flow conditions

This paper presents a theoretical study of the effects of Poiseuille Reynolds number and eccentricity ratio on the performance of four-pad hydrostatic squeeze film dampers. The finite difference method has been used to solve Reynolds equation based on Constantinescu’s turbulent lubrication theory. The numerical results obtained are analysed and compared between three and four-lobe hybrid journal bearings. The computed results indicate that the performance of a hydrostatic squeeze film damper loaded between pads is significantly influenced by the flow regimes. The results presented in this work can be useful to the bearing designers.     

Inverse approach for calculating pressure and viscosity in pure squeeze EHL motion of circular contacts

The inverse approach is proposed to the pure squeeze EHL motion of circular contact problems, where the pressure is approximated by polynomial form in terms of the radial coordinate and time to provide a smoothing algorithm in calculating pressure from the elasticity equation. The least-squares method is used to calculate the optimum value of the pressure–viscosity index from the transient Reynolds equation. Results show that the estimated pressure can be obtained accurately with a few measuring film thickness points, but it is hard to obtain the correct viscosity for the direct inverse method. By using the inverse approach, even though the measurement error in the film thickness is present, the fluctuations in the pressure can be overcome, and it predicts the pressure–viscosity index with very good accuracy. The post-impact high-pressure condition for the constant load case is suitable to evaluate the pressure–viscosity index in a wide range along the radial axis with very good accuracy. Subsequently the inverse approach is successfully used to estimate the pressure distribution resulting from the film thickness map from the interferometry measurements. The agreement between the actual value of the test fluid and the estimated value is quite good.     

Simple equation for elastohydrodynamic film thickness under acceleration

A simple approximation of EHD film thickness under varying speed conditions is proposed. The equation is based on continuity of flow, by which the film formed at the contact inlet moves downstream within the contact with little subsequent change in its thickness even though the boundary velocities are changing. The approximation is supported by experimental results of non-steady state film thickness measurement using ultra-thin film interferometry. It is also shown by numerical simulation that the approximation holds for film thickness in the rigid piezoviscous regime under line contact so long as the squeeze film effect is insignificant.     

The dynamic behaviour of squeeze films in one-dimensional porous journal bearings lubricated by a micropolar fluid

The generalized Reynolds equation governing the pressure distribution for a micropolar lubricant in a dynamically loaded porous journal bearing is derived and applied to one-dimensional squeeze film journal bearings operating under a cyclic load. The analysis indicates how the microstructure in the lubricant, the permeability of the bearing material and the bearing wall thickness influence the operating eccentricity ratio.     

Numerical solution of couplestress finite Reynolds equation for squeeze film lubrication of partial porous journal bearings

Abstract

In this paper, the general Reynolds equation of finite porous journal bearing lubricated with couplestress fluid is solved numerically for the assessment of dynamic characteristics of the bearings. The Reynolds type equation governing the steady performance is obtained and solved numerically by finite difference technique. From the numerical results, it is observed that the effect of couple stresses is to increase the load carrying capacity and to lengthen the squeeze film time as compared to the corresponding solid case. The effect of permeability is to reduce the load capacity and to decrease the squeeze film time as compared to the solid case.     

Approximate closed-form solution of the synovial fluid film force in the human ankle joint with non-Newtonian lubricant

The aim of this paper is to propose an approximate closed form lubrication model of the human ankle joint by taking into account the porosity of the cartilage matrix and the non-Newtonian behaviour of the synovial fluid. The model is based on the theory of squeeze lubrication and introduce an original modified Reynolds equation obtained modelling the synovial fluid as a couple-stress fluid and the synovial fluid transport across the articular cartilage by using a modified Darcy's equation. This approach gives the advantage to obtain an analytical expression of the synovial pressure field and of the non-stationary fluid film force acting in the synovial joint during the squeeze motion in terms of couple-stress parameter, film thickness, and porosity parameter.     

Comparative performance of squeeze film air journal bearings made of aluminium and copper

Two tubular squeeze film journal bearings, made from Al 2024 T3 and Cu C101, were excited by driving the single-layer piezoelectric actuators at a 75-V AC with a 75-V DC offset. The input excitation frequencies were coincident with the 13th modal frequency, at 16.32 and 12.18 kHz for the respective Al and Cu bearings, in order to produce a ‘triangular’ modal shape. The paper also provided a CFX model, used to solve the Reynolds equation and the equation of motion, to explain the squeeze film effect of an oscillating plate with pressure end leakage. The dynamic characteristics of both bearings were studied in ANSYS and then validated by experiments with respect to their squeeze film thickness and load-carrying capacity. It was observed that whilst both bearings did levitate a load when excited at mode 13, the Al bearing showed a better floating performance than Cu bearing. This is due to the fact that the Al bearing had a higher modal frequency and a greater amplitude response than the Cu bearing.     

Micropolar fluid squeeze film lubrication of finite porous journal bearing

In this paper, the effect of micropolar fluid on the static and dynamic characteristics of squeeze film lubrication in finite porous journal bearings is studied. The finite modified Reynolds equation is solved numerically using the finite difference technique and the squeeze film characteristics are obtained. According to the results obtained, the micropolar fluid effect significantly increases the squeeze film pressure and the load-carrying capacity as compared to the corresponding Newtonian case. Under cyclic load, the effect of micropolar fluid is to reduce the velocity of the journal centre. Effect of porous matrix is to reduce the film pressure, load-carrying capacity and to increase the journal centre velocity.     

Effect of roughness on hydromagnetic squeeze films between porous rectangular plates

The theoretical investigations made in this paper are to study the combined effects of unidirectional surface roughness and magnetic effect on the performance characteristics of a porous squeeze film lubrication between two rectangular plates. The stochastic Reynolds equation accounting for the magnetic effect and randomized surface roughness structure is mathematically derived. The expressions for dimensionless pressure, load carrying capacity and squeeze film time are obtained. Results are computed numerically and it is observed that a roughness effect enhances pressure, load carrying capacity and squeeze film time.     

水润滑轴承材料弹流润滑性能比较研究

利用考虑惯性力的Reynolds方程,对水润滑条件下的实验橡胶滑块与钢环的弹流润滑问题进行了数值模拟,并分别与塑料、陶瓷材料的数值模拟结果进行了对比分析。结果表明,在水润滑条件下,惯性力对水膜压力的影响很小,而对水膜厚度及温度的影响很大。同样情况下,考虑惯性力时,最小膜厚增加,最高温度降低。橡胶/钢摩擦副中,惯性力对膜厚的影响是不可忽略的。陶瓷/钢摩擦副中,考虑惯性力时对温度影响更大。     

基于Evans-Johnson流变模型粘塑性流体弹流润滑的数值计算

推导了基于Evans-Johnson流变模型的雷诺方程,并进行了数值求解,将数值计算结果与基于理想粘塑性流变模型的数值结果进行了比较.结果表明,基于Evans-Johnson流变模型和基于理想粘塑性流变模型所得到的油膜压力分布没有本质的区别,但基于二者的油膜厚度却有很大的不同;在大滑滚比的工况下,由前者所得的中心膜厚度比由后者所得的中心膜厚度低,表明在考虑润滑剂粘塑性的弹流润滑研究中,选用合适的润滑剂流变模型很重要。     

Elastohydrodynamic lubrication of circular contacts at pure squeeze motion with non-Newtonian lubricants

In this study a numerical method for general applications with non-Newtonian fluids is developed to investigate the pure squeeze motion in an isothermal elastohydrodynamic lubricated spherical conjunction under constant load conditions. The coupled transient modified Reynolds, the elasticity deformation, and the load equilibrium equations are solved simultaneously. Computer simulation is carried out to investigate the effects of flow rheology and operations on the relationship between the pressure and film thickness distributions. The simulation results reveal that the larger the flow index (n), the larger the film thickness and the smaller the maximum central pressure. This results in larger time needed to obtain maximum central pressure. In addition, the elastic deformation is more significant for the lower flow index. Therefore, the smaller the flow index becomes, the greater the difference between the hydrodynamic lubrication (HL) solution and elastohydrodynamic lubrication (EHL) solution becomes.     

微观织构配流副热-流-固耦合润滑特性

通过建立轴向柱塞泵配流副的几何模型,利用雷诺方程推导了配流副的油膜压力方程,采用有限差分法和松弛迭代法求解雷诺方程。利用FORTRAN语言编程求解,利用MATLAB语言对油膜厚度、压力、温度分布进行了仿真研究。结合油膜厚度方程、雷诺方程、能量方程、弹性变形方程、黏温黏压方程和密度温压方程,仿真微观织构配流副的热弹流润滑特性。研究表明：配流副油膜厚度增大,最大油膜压力减小,最高温度值减小;配流副的热-流-固耦合效果随油膜间隙收敛逐渐明显,在最小油膜厚度处达到最大,并且,油膜压力值达到最大;加工微观织构可以显著改变配流副的油膜压力和温度分布。