A Porous Hydrostatic Gas Bearing for Use in Miniature Turbomachinery

An analytical program was conducted to establish recommended types of gas-lubricated journal bearings for use in miniature cryogenic turbomachinery. Very high rotative speeds, and the limiting damping properties of gas, indicated that fractional frequency whirl is prevalent, and the most difficult problem to overcome. Of the many journal bearing types investigated, the tilting pad hydro-dynamic and porous hydrostatic journal bearings were suited to the application.

A novel spring mounted, three shoe, porous hydrostatic bearing is discussed in terms of design and experimental results. A 1/2 inch diameter journal bearing is subjected to loading and speeds to 700 grams and 65,000 rpm, respectively. Excellent performance in terms of load capacity, power loss, and flow are indicated. Orbit motions of the floated bearing with respect to the supported shaft demonstrate desirable stability characteristics for the range of tests.     

Thermal Behavior of a Worn Tilting Pad Journal Bearing: Thermohydrodynamic Analysis and Pad Temperature Measurement

Abstract

Tilting pad journal bearing (TPJBs) have been widely used in rotating machinery such as compressors and turbines due to their superior stability compared to that of conventional fixed geometry bearings. As the adoption of TPJBs increases, various failure mechanisms related to TPJBs have been reported and pad wear is a frequently reported one. Pad wear causes geometry changes of the bearing, which can sometimes result in entire system failure. Therefore, it is important to detect the problem in the early stage to prevent unexpected system shut down. The objective of the current research is to investigate the influence of pad wear on the pad temperature, which is one of the widely used condition monitoring methods of TPJBs. For the theoretical investigation, thermohydrodynamic (THD) analysis was conducted by solving the generalized Reynolds equation and 3D energy equation. The developed THD model was validated by comparing the results with test data available in the literature. The results of the analysis showed that the temperature of the loaded pad increases and that of the unloaded pad decreases when wear occurred on loaded pads. In addition, the minimum film thickness also decreases with the wear depth. The validation test conducted with a test rig which mimics axial turbine where a test rotor was supported by two TPJBs. The test bearing consists of five pads with diameter of 60 mm and a resistance temperature detector (RTD) was installed in the pad for temperature monitoring. The test was performed by replacing the two loaded pads with the worn pad. The test result for TPJB with wear depth of 30 μm showed that the temperatures of the loaded pads were 8°C higher and that of the unloaded pad was 2.5°C lower than that of the normal TPJB. Additionally, the predicted pad temperature shows good agreement with the measured pad temperatures.     

Dynamic analysis of a rigid rotor supported by three-pad hydrostatic squeeze film damper lubricated with ferrofluid

This work describes an analytical study on the dynamic behaviour of a three-pad hydrostatic journal bearing lubricated with ferrofluids. Each pad is fed with an external pressure through a capillary restrictor-type hydraulic resistance. Ferrofluid or magnetic fluid is a colloidal dispersion of magnetic nano-particles in a carrier liquid. In this study, a non-linear method was performed using Jenkins model in order to investigate the effect of ferrofluids lubrication on the vibrations amplitude and the transmitted forces of hydrostatic squeeze film dampers. The results presented in this paper showed that the ferrofluid lubrication is useful in controlling the bearing vibrations and transmitted forces. The results illustrated in this work are expected to be quite useful to the bearing designers.     

MHD couple stress squeeze film characteristics between sphere and plane surface

Abstract

In this paper, the effect of non-Newtonian couple stress fluids on the magnetohydrodynamic (MHD) squeeze film characteristics between a sphere and a plane surface is analysed. By taking into account the couple stresses due to the presence of microstructure additives in the lubricant and the magnetic effects due to the magnetisation of the couple stress fluid, the non-Newtonian couple stress MHD Reynolds type equation is derived. The numerical solutions for the MHD squeeze film characteristics are presented for various values of couple stress parameter, and magnetic Hartmann number. The results indicate that the influences of couple stresses and the magnetic effects on the squeeze film characteristics are significantly apparent. It is concluded that the MHD couple stress fluids have better lubricating qualities than the corresponding Newtonian case.     

Investigation into the effect of piston ring seals on an integrated squeeze film damper model

This research presents an advanced squeeze film damper model that integrates piston ring seal geometry, fluid inertia, and film cavitation to study their combined features. The configuration of the piston ring seal is inspected, and different sealing scenarios are discussed. The flow rate in the seal arrangement is determined on the basis of the pressure gradient according to thin film theory. Moreover, the governing equation for the flow in the film land that considers fluid inertia is solved using the linear complementarity problem method to address the cavitation phenomenon. Validation is performed by comparing the model prediction with long bearing and short bearing models under different seal dimensions. Results show that an oversized gap in the seal grooves and a large frictional coefficient may lock the piston ring seal in the seal groove and thus reduce seal efficiency.

     

Characteristics of non-newtonian power law lubricants in step bearings and hydrostatic step seals

The effects of stepped film-thickness on the various characteristics of squeeze films, conical bearings and hydrostatic step seals, using a power law fluid as lubricant have been investigated. It has been shown that the load capacities of squeeze film bearings decrease and those of conical bearings and step seals increase, with the increase in the step height. With a hydrostatic step seal, the load capacity increases as the flow behaviour index of the power law fluid increases.     

Theoretical Analysis of Piston-Ring Lubrication Part I—Fully Flooded Lubrication

A one-dimensional analysis for lubrication between the piston ring and cylinder wall has been developed. A fully flooded inlet condition and axisymmetric geometry are considered. The piston ring is treated as a reciprocating, dynamically-loaded bearing with combined sliding and squeeze motion. A system of two nonlinear differential equations is used to model the lubrication including the Reynolds cavitation boundary condition. A numerical procedure is then developed to obtain the cyclic variations of film thickness, frictional force, power loss, and oil flow across the ring.

Results are presented for a typical automotive engine. The effects of ring profile, ring tension, and engine speed are examined. It is shown that this analysis can be used to study the influence of ring design parameters in order to improve the design of the ring pack in reciprocating engines.     

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.     

Hydraulic Squeeze Bearing

Prior researchers find that: Where one of two horizontal parallel plates immersed in a fluid is forced to oscillate up and down, a load may be carried, providing the fluid is compressible. Application of Reynolds equation to such a squeeze film bearing supports the condition of compressibility.

However, analysis of the squeeze film bearing, including inertia terms in the Navier-Stokes equations, removes the restriction on compressibility.

Theoretical design of a hydraulic squeeze bearing driven sinusoidally shows that load capacity is improved over a similar gas squeeze bearing under usual design conditions, provided cavitation is prevented. Two cases are considered of a fixed and a free bearing. Torque, work input, and the effects of centrifugal force are analysed.     

并联封闭式挤压油膜阻尼器的多孔质可倾瓦轴承性能分析与试验验证

鉴于封闭式挤压油膜阻尼器(Hermetically sealed squeeze film damper, HSFD)良好的阻尼性能，并联HSFD的多孔质可倾瓦轴承(Porous tilting pad bearing, PTPBs)有望用于兆瓦级涡轮机械，具有广泛的应用前景。呈现了一种HSFD等效刚度和等效阻尼的计算方法，该方法成功体现了阻尼器刚度和阻尼的“频率依赖”特性。将HSFD与多孔质瓦块模型耦合建立了该轴承的综合理论模型，并进一步验证了该模型的正确性。最后研究了供气压力、轴承间隙以及是否安装HSFD等对轴承静动态特性的影响。结果表明，HSFD的存在大幅提高了轴承的阻尼水平和稳定性。     

Nanosys-1000机床静压止推轴承流场分布规律及承载特性

为了提高Nanosys-1000非球面曲面光学零件超精密加工机床加工精度,研究了机床核心部件静压止推轴承内流场分布规律,进而揭示其承载特性。利用ANSYS/Fluent软件建立对称结构静压止推轴承扇形油垫的仿真模型,采用层流模式对进油压力为1.3~1.9 MPa、油膜厚度为20~36 μm的油垫流场分布规律与承载特性进行分析。研究结果表明：油垫内压力在油腔区域比较均匀,沿封油边呈线性下降;油膜承载力随油腔压力线性增长,且在同一进油压力下,油膜厚度越小,油膜承载力越大,进油压力为1.5 MPa时,油膜厚度从36 μm减小到20 μm,油腔压力从3.05×10⁵ Pa增加到8.02×10⁵ Pa,油膜承载力相应地从880 N增加到2 109 N;同一负载即油膜承载力下,进油压力越高,油膜厚度越大,油膜承载力为1 320 N时,进油压力从1.3 MPa增加到1.9 MPa,油膜厚度从26 μm增加到30 μm;同一油膜厚度下,进油压力越高,润滑油流量越大,油膜厚度为28 μm时,进油压力从1.3 MPa增加到1.9 MPa,润滑油流量从0.179 L/min增加到0.231 L/min。相关研究结果在研制的Nanosys-1000非球面曲面超精密加工机床静压止推轴承上得到了验证。     

两种挤压油膜阻尼器的刚度和阻尼特性

通过对以窄阻尼器为代表的普通型挤压油膜阻尼器 (SFD)和以四油腔垫式阻尼器为代表的静压型挤压油膜阻尼器 (HSFD)的动力学参数的对比分析 ,获得了两种阻尼器的刚度和阻尼特性。结果表明 ,相对于纯阻尼器 SFD,HSFD在许多方面具有优越性     

Micropolar fluid squeeze film lubrication between rough anisotropic poroelastic rectangular plates: special reference to synovial joint lubrication

Abstract

The effect of anisotropic permeability on micropolar squeeze film lubrication between poroelastic rectangular plates is studied. The non-Newtonian synovial fluid is modelled by Eringen’s micropolar fluid, and the poroelastic nature of cartilage is taken in to account. The stochastic modified Reynolds equation, which incorporates the elastic as well as randomised surface roughness structure of cartilage with micropolar fluid as lubricant, is derived. Modified equations for the mean fluid film pressure, mean load carrying capacity and squeeze film time are obtained using the Christensen’s stochastic theory for the study of roughness effects. The effects of surface roughness, micropolar fluid and anisotropic permeability on the squeeze film characteristics of synovial joint are discussed. It is found that the surface roughness effects are more pronounced for micropolar fluids as compared to the Newtonian fluids, and the anisotropic nature of permeability of cartilage off-squares the plate size for optimum performance.     

Mechanisms of Chemical-Mechanical Polishing of SiO2 Dielectric on Integrated Circuits

One of the fundamental mechanisms of chemical-Mechanical polishing (CMP) is the mechanical interaction between the wafer and polishing pad. This interaction was simulated in experiments. The vertical displacement of the wafer with respect to the polishing pad, the fictional drag of the wafer against the pad, and the pressure of the slurry trapped between the wafer and pad were measured. These experiments were performed over a range of commercially common CMP conditions. In addition, polishing rates were measured for CMP performed under induced hydrodynamic conditions where the wafer was separated from the pad by a film of slurry.

It was found that no appreciable polishing occurred under hydrodynamic CMP conditions. Under commercial CMP conditions, it was found that the wafer contacts the polishing pad asperities as evidenced by near-zero wafer displacement and high friction coefficients (?0.4). It was also found that pad conditioning (intentional roughening) causes a suction force to develop between the wafer and pad. This suction force draws the wafer into further contact with the pad, by as much as 20 μm, and corresponds to peak slurry vacuum pressures of 12 kPa (1.7 psi).     

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.     

The Behavior of the Centrally Pivoted Thrust Bearing Pad with Hydrostatic Recesses Pressurized by a Constant-Rate Flow

The tilting behavior of the centrally pivoted, externally pressurized tilting thrust pad is investigated. The pressure distribution in the oil film is obtained by solving the Reynolds' equation which takes into account the external pressurization induced by a constant-rate flow. The relation between the size of the hydrostatic recess and the tilt angle of the pad is described. Calculations show that a pad with pressure recesses may have a negative tilt angle, depending on the size of the recess. The pressure variation around the hydrostatic pressure recess causes the moment to force the pad to tilt backward. At high shaft rotational speeds, the pad tilts backward too much and eventually fails to support the load. The hydrostatic pressure recess that is utilized to avoid the metal contact may cause this. The result was confirmed by experiments.     

An isoviscous,isothermal model investigating the influence of hydrostatic recesses on a spring-supported tilting pad thrust bearing

Tilting-pad hydrodynamic thrust bearings are used in hydroelectric power stations around the world, reliably supporting turbines weighing hundreds of tonnes, over decades of service. Newer designs incorporate hydrostatic recesses machined into the sector-shaped pads.With the aid of external oil pressurisation at low rotational speeds, oil film thickness is increased, thereby reducing friction and wear to the benefit of service life and reliability. It follows that older generating plants, lacking such assistance, stand to benefit from being retrofitted with hydrostatic lubrication systems. The design process is not trivial however – the need to increase the groove area to permit spontaneous lifting of the turbine under hydrostatic operation conflicts with the need to preserve performance of the original plane pad design. A haphazardly designed recess can change the pressure distribution of the oil film in such a way as to tilt the pad away from its optimum position. This may lead to reduced oil film thickness and increased temperature, which is concomitant with reduced mechanical efficiency and increased risk of damage to the bearing surfaces. It is therefore, inadvisable to ignore the presence of grooves in simulations. In this work, a numerical study of a sector-shaped pad is undertaken to understand how recess size and shape can affect the performance of a typical bearing. An isoviscous, isothermal model has been used in this instance because the operating conditions of the turbine in question were shown not to be severe enough to warrant the computational expense of a fully coupled thermoelastic hydrodynamic model.     

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.     

Optimization of Pocket Geometry for Friction Reduction in Piston–Liner Contacts

It has recently been shown that rectangular surface pockets are effective in reducing friction in a piston–liner type contact, providing that they are oriented with their long axis transverse to the sliding direction so that entrained features fit completely within the contact area (Vl?descu, et al., Tribology International, 82, 28–42, 2015; Vl?descu, et al., Tribology International, 115, 140–153, 2017). The aim of the current study was to identify the optimal geometric parameters of theses rectangular features. To do this, a friction rig that simulated a piston–liner contact under highly controlled conditions was used to test a series of textured specimens with pockets of different depth, breadth and density. Each of these geometric parameters was varied and tested independently, while keeping the other two constant. Experimental conditions were set in order to place the contact in different lubrication regimes.

Results were analyzed to determine a set of criteria for the optimum pocket geometry; however, this was shown to change depending on the test conditions and should therefore be adjusted depending on the position along the stroke. Specifically, at low speed when the contact is operating under boundary lubrication, pockets should be deep, wide, and densely spaced. This confirms recent findings, which suggested that, in this regime, pocket volume is often a more critical parameter than depth, width, or spacing individually. Conversely, under mixed lubrication toward the transition to the full film regime, pockets should be narrow and sparsely spaced. These results also explain the difficulties encountered in several previous studies that attempted to define a single optimum pocket geometry.

Finally, the impact of pocket position relative to reversal was assessed for various lubrication conditions. This revealed how pockets should be placed close to, but not directly at, top and bottom dead center to provide a beneficial squeeze film, which is present at reversal.     

The Isothermal Lubrication of Cylinders

When the hydrodynamic problem of cylinder lubrication is considered, two distinct types of solution emerge. For light loads the cylinders retain their unloaded geometry; the Martin solution for this condition is well known. When the contact forces are large, significant elastic deformation may occur; the resulting elastohydrodynamic regime has been extensively analyzed in recent years.

Equations are now available for the calculation of minimum film thickness in the “rigid” and “elastic” situations. In this paper computing methods appropriate to each range of conditions are summarized, and the nature of the solutions is considered in some detail. In particular the valid range of application of the “rigid” and “elastic” film thickness relationships is discussed. An intermediate range of conditions between the “rigid” and “elastic” regimes is defined.

Finally, a chart is presented to enable a particular problem to be located in the “rigid,” “intermediate,” or “elastic” zones.