Squeeze films in full porous metal bearings

The behaviour of squeeze films in porous journal bearings under a steady load is analysed. A full journal bearing with a non-rotating journal is considered. The Reynolds equation governing the pressure in the film region is modified to take account of the mass exchange of the lubricant between the film and the bearing matrix. In the case of thin-walled bearing (H?R), the modified Reynolds equation takes a simpler form. However, since this equation cannot be solved directly as applied to a finite bearing, solutions in a closed form are found both for the long bearing and narrow bearing approximations. It is found that the permeability of the bearing matrix and the wall thickness of the bearing adversely affect the load capacity and greatly reduce the time needed for the journal to attain a given eccentricity. With a permeable bearing, there is the possibility of the journal coming into contact with the bearing (ε=l) in a finite time. Generally the performance of a long bearing is better than that of a narrow bearing.     

TEHD Analysis for Tilting-Pad Journal Bearings Using Upwind Finite Element Method

A general approach for incorporating heat transfer and elastic deformation effects into a tilting-pad journal bearing simulation model is presented. A global analysis method is used, which includes variable viscosity and heat transfer effects in the fluid film, elastic deformation and heat conduction effects in the pads, and elastic deformation effect in the pivots. The two-dimensional variable viscosity. Reynolds equation produces pressure distributions in the axial and circumferential directions. The energy equation is two-dimensional, assuming that the temperature variation in the axial direction is negligible. The elasticity and heat conduction models are also two-dimensional, being in the midline cross-section of the bearing, including the circumferential and cross-film directions. An upwind technique is used in the finite element formulation of the energy equation to remove numerical instability due to the convective term. Simulation results are compared with the test and predicted values of previous researchers.     

Thermal Structural Effects in a Gas-Lubricated Foil Journal Bearing

A theoretical model for gas-lubricated foil journal bearings that incorporates thermal structural effects is presented. Bending and membrane effects in the top foil resulting from temperature are included along with thermal expansion of the journal, subfoil, and bearing housing. The model includes thermal transport through the journal, foils, and bearing housing. Pressure in the gas film is predicted using the Reynolds equation, and a thermal bulk flow model is used to predict temperature. The results demonstrate that models will overpredict film thickness along the side edge of a bearing if thermal strain in the top foil is not included. In addition, the results show the need for a three-dimensional thermal flow model at the trailing edge of a bearing when backflow occurs.     

Effects of couple stresses in the cyclic squeeze films of finite partial journal bearings

Based upon the microcontinuum theory, the present paper is to theoretically study the pure squeeze-film behavior of a finite partial journal bearing with non-Newtonian couple-stress lubricants operating under a time-dependent cyclic load. To take into account the couple stress effects resulting from the lubricant blended with various additives, the modified Reynolds equation governing the film pressure is obtained from Stokes equations of motion. The film pressure is numerically solved by using the Conjugate Gradient Method. Bearing characteristics are then calculated from the nonlinear motion equation of the journal. According to the results obtained, the effects of couple stresses result in a decrease in the value of eccentricity of the journal center. The finite partial bearing with a couple stress fluid as the lubricant yields an increase in the minimum permissible clearance and provides a longer time to prevent the journal-bearing contact.     

Influence of Mixed-Lubrication and Rough Elastic-Plastic Contact on the Performance of Small Fluid Film Bearings

A previously developed deterministic elastohydrodynamic (EHD) numerical model for small fluid film bearings functioning in the mixed lubrication regime is extended in this work by considering the rough contact. Several simplifying hypotheses are made: the shaft is considered rigid and smooth, turning at low speeds (isothermal regime), and the pad is assumed to have an elastic-perfectly-plastic behavior. The Reynolds equation is solved on a very fine mesh and the elasto-plastic pad deformation caused by the hydrodynamic pressure is taken into account. A deterministic active set-based method is used for determining the contact pressure, the contact extent, and the corresponding deformation. The results are presented for a partial journal bearing configuration, with a linear shaft velocity of 0.47 m/s under specific pressures varying up to 50 MPa. Two pad materials are considered, and the lubricant is either isoviscous or piezoviscous oil. The simulation results, presented as a function of the bearing specific pressure, include eccentricity, the film thickness, the friction torques, the contact extent, etc. Stribeck curves showing the evolution of the friction coefficient in the hydrodynamic and mixed lubrication regimes are also discussed.     

Gas-dynamic foil bearing model

A method is developed to calculate the characteristics of gas-dynamic bearings of rotors of gas-turbine engines and gas-turbine units. The method takes into account the contact interactions between the shaft journal, the fluid film, and the elastic bearing elements. The problem of multidisciplinary mathematical simulation of the elastic gas-dynamic contact is formulated and solved to determine the parameters of lubrication and deformations of the shaft and bearing. The considerable nonlinearity of the problem is governed by the equations describing the fluid flow in the bearing and the features of the elastic contact during deformation of the bearing elements. The calculation of the fluid-film flow in the bearing is based on the solution of the nonlinear two-dimensional Reynolds equation for a compressible fluid. The method of consecutive loading with error correction that within the interval prompts to the linearized Reynolds equation solution for fluid film pressure increment is used. The results of calculation of the fluid-flow parameters in the clearance between the shaft and the bearing are compared with the results obtained by solving the fluid-flow problem in a bearing modeled with the Navier-Stokes equations with the STAR-CD software. The stress-strain state of the elastic bearing elements is studied with the finite element model taking into account the contact interaction between the foils themselves and with the bearing race. The pressure distribution and the clearance in the shaft are determined iteratively by the coupled solution of the fluid flow and bearing foil deformation problems. Bearing stiffness characteristics, its carrying force and attitude angle are determined versus shaft journal displacement value and direction. It is shown that the stiffness characteristics of the bearing depend on the direction of displacement of the shaft journal in the bearing. The influence of the bearing elastic element deformations on the support load carrying capacity and the stiffness characteristics are studied. The results yielded by the calculations with the developed method are compared with those when the fluid-layer thickness in the bearing was calculated using the analytical model proposed by H. Heshmat and co-authors.     

The Stability Margin of a Roughened Hole-Entry Hybrid Journal Bearing System

The present work describes a theoretical investigation into the effect of surface roughness on the stability margin of an orifice-compensated, hole-entry hybrid journal bearing system. A modified form of the average Reynolds equation is used for the solution of a lubricant flow field in the clearance space of a rough journal bearing system. The effects of surface roughness parameter (Λ), variance ratio (V?_rj), and the surface orientations (γ) on the bearing flow, load-carrying capacity, and stability threshold speed margin are studied. The study indicates that the bearing configurations having surface roughness on one of the opposing surfaces (stationary or moving roughness) show an opposite trend between stability threshold speed margin and load-carrying capacity. However, the bearing configurations having transverse- and isotropic-type roughness patterns on both bearing and journal surfaces provide an improved value of both stability threshold speed margin and load-carrying capacity only when the surface roughness has a variance ratio value between 0.49 and 0.59 for the transverse roughness pattern and between 0.59 and 0.84 for the isotropic roughness pattern.     

Modeling of Gas Thermal Effect Based on Energy Equipartition Principle

In the present article, a gas thermal effect is modeled based on the energy equipartition principle. Two new independent state equations for an ideal gas are developed that provide a new way to analyze thermal effects in gas lubrication. Furthermore, the energy equation is derived for gas lubrication and the analysis of thermal effects is carried out on a gas spiral thrust bearing and a gas hydrostatic journal bearing. The results show that gas temperature increases significantly in the lubricated region at high speed for both the thrust and hydrostatic journal bearings, and the thermal effect positively influences the load capacity of the thrust bearing. The gas expansion effect makes the gas temperature decrease in the hydrostatic journal bearing, and the gas temperature decreases with an increase in the inlet pressure.     

导轴承性能热流体动力分析

建立了导轴承性能热流体动力分析的数学模型,应用有限元法对表示油膜压力的Reynolds方程及表示油膜温度的Energy方程和表示温度和粘度关系的粘温方程进行了联立求解,获得了多瓦导轴承的瓦块压力分布,温度分布及其它轴承静态和动态参数.并根据这些参数对多瓦导轴承的性能作了分析,其结果对该轴承设计具有一定的指导作用,并对运行过程具有预测作用.     

滑动轴承的应力分析

本对发动机的滑动轴承进行了计算,求解了滑动轴承的雷诺方程,粘度方程,密度方程与载荷方程,得到了压力分布与油膜厚度分布,进而通过接触力学分析得到轴承衬内的应力分布。应力分布是影响材料的塑性变形,并对分析滑动轴承的胶合失效有实际意义,因此建议用最大Mises应力来指导滑动轴承的设计。     

Journal Design Considerations for Turbomachine Shafts Supported on Foil Air Bearings

Foil air bearings can offer substantial improvements over traditional rolling element bearings in many applications and are attractive as a replacement to enable the development of advanced oil-free turbomachinery. In the course of rigorous testing of foil journal bearings at NASA Glenn Research Center, shaft failure was repeatedly encountered at high ambient temperature and rotational speed, with moderate radial load. The cause of failure is determined to be excessive non-uniform shaft growth, which increases localized viscous heating in the gas film and eventually leads to a high-speed rub and destruction of the bearing and journal. Centrifugal loading of imbalance correction weights and axial temperature gradients within the journal due to the hydrodynamic nature of the foil bearings, determined by experiment and finite element analysis, are shown to be responsible for the non-uniform growth. Qualitative journal design guidance is given to aid in failure prevention.     

Computational Mixed TEHL Model and Stribeck Curve of a Journal Bearing

The aim of this article is to propose a model capable of estimating the friction along a heavily loaded journal bearing under mixed and hydrodynamic lubrication. The finite element analysis–computational fluid dynamics (FEA-CFD) model takes into consideration the effect of solid deformations, the asperity contact phenomena, and the influence of metal–metal contact in the Reynolds equation. The Stribeck curve for a plain journal bearing under different operational conditions is calculated and compared to experimental results. The major contribution of the article is the novelty of including mixed lubrication, high-load conditions, and thermal effects in a single computational steady-state model. This comprehensive model, not limited to a specific range of operational conditions, can help during design and for health condition monitoring.     

考虑不同加速工况的滑动轴承的启停性能分析*

滑动轴承的摩擦磨损主要发生在启停阶段。为了研究启停工况下的滑动轴承的摩擦学性能,建立一种面向径向滑动轴承的混合润滑数值分析模型。采用质量守恒边界条件的雷诺方程求解流体压力,采用Greenwood和Tripp接触模型预测固体表面接触,而通过Johnson载荷分配概念将润滑模型和接触模型联系起来,从而实现对滑动轴承在启停工况下从混合润滑过渡到动压润滑的摩擦学行为分析。利用该模型,研究轴承系统在启停阶段从边界润滑、混合润滑到动压润滑演化过程中的摩擦学性能;以径向滑动轴承系统为例,结合不同的轴承转速变化函数,分析轴承加速对轴承启停性能的影响;同时研究工作工况、润滑油温度、轴承的结构参数对轴承启停性能的影响。结果表明：轴承启动加速度在合理范围内越大越好,能使轴承更快进入动压润滑;较高的转速、较低的润滑油温度和较大的径向轴承间隙能使轴承拥有更好的启停性能。     

动压气体轴承-转子系统的分岔和混沌

基于非线性动力学理论,研究了气体动压轴承-转子系统的不平衡响应及分岔行为。建立了与时间相关的非线性气体动压轴承的压力分布模型和气体动压轴承-刚性Jeffcott转子系统的动力学模型。运用有限差分法和逐次超松弛迭代法求解动压气体润滑雷诺方程;运用轨迹图、Poincaré映射图、时间历程图、频谱图和分岔图研究了有限宽气体轴承支承的非线性转子系统的不平衡响应及分岔;数值模拟结果揭示了系统存在复杂多样的非线性现象,这对气体润滑轴承支承的实际轴承—转子系统的设计提供了理论依据。     

Misaligned journal effects in liquid hydrostatic non-recessed journal bearings

The performance characteristics of a capillary-compensated hole-entry hybrid misaligned journal bearing have been studied theoretically. The journal of the bearing is allowed to tilt on an axial plane containing the load vector and on a plane perpendicular to an axial plane containing the load vector. The journal misalignment has been accounted for by defining a pair of misalignment parameters σ and δ. The finite element method has been used to solve Reynold's equation governing the lubricant flow field in the clearance space of the journal bearing. Static and dynamic performance characteristics are presented for the different representative values of the journal misalignment parameters for both hydrostatic and hybrid modes of operation of the bearing. The bearing performance characteristics are also compared for the two hole-entry bearing configurations so as to facilitate the selection of a suitable bearing configuration by the designer. The study suggests that the journal misalignment significantly affects the performance of the hole-entry journal bearing, and for a more accurate prediction of the bearing performance it must be considered in the analysis.     

Calculation of a Safety Margin for Hydrogenerator Thrust Bearings

The purpose of this paper is to present the two-dimensional linear stability analysis considering the fluid flow in both full film and cavitation regions for a plain cylindrical journal bearing. The Lund's infinitesimal perturbation procedure is applied to Elrod's universal equation for evaluation of unsteady pressure gradients. Based on JFO theory, the pressure distribution, film rupture, and reformation boundaries can be obtained using Elrod's universal equation, for a given operating position of the journal. In this work, it is assumed that for infinitesimal perturbation of a journal about the equilibrium position, the film rupture and film reformation boundaries are the same as those obtained for steady state. However, the unsteady pressure gradients in the full film region are evaluated taking into consideration the perturbed flow parameters in the cavitation region, i.e., at both rupture and reformation boundaries. The linearized stiffness and damping coefficients, whirl frequency ratio, and threshold speed for various values of eccentricity and L/D ratios are obtained for a plain cylindrical journal bearing with an axial groove along the load line. Measured data of dynamic coefficients for a 120° partial arc bearing are chosen for comparison with this work. Results show good agreement between the theoretical and experimental results.     

Rigidity and damping characteristics of hydrodynamic sliding bearing with deformable working surfaces

The model of a hydrodynamic sliding bearing has been developed that takes into consideration the effect of the deformation of sliding surfaces on the bearing characteristics. The deformations of the sliding surfaces are determined when solving the problem of elastohydrodynamic contact of the journal and bearing with account for the pressure in the lubricating film. Variation in the clearance size at the deformation of the bearing and shaft surfaces is found by iterations when solving jointly the problems of lubricant flow and working surface deformation. Elastic deformations of the working surfaces are calculated using a two-dimensional boundary element model and a three-dimensional finite element model of the shaft and bearing. The method of finite elements is applied to calculate the parameters of lubricant flow in the bearing based on the solution of Reynolds equation in the disturbed form. The rigidity and damping characteristics of the sliding bearing with the deformable surfaces are compared to those of the bearing with the rigid surfaces; the results of the two-dimensional model of bearing deformation are compared to those of the three-dimensional one.     

An Experimental Comparison of Two Steadily Loaded Plain Journal Bearings

A potentially powerful effect on the characteristics of plain journal bearings is local thermal deformation of the bearing surface. Although there are a few analyses that consider the effect, it is ignored by most journal bearing codes used by industry. There is also almost no experimental data in the literature that focuses on this effect. To generate such data, two identical, 101 mm dia., 57 mm long bearings—one fabricated from steel and one from bronze—have been tested in a precision journal bearing test rig. Comparisons between shaft displacement data for steady loading of the two bearings show that the deformations are important to consider.     

Analysis of Noncircular Hole-Entry Capillary-Compensated Hybrid Journal Bearing with Micropolar Lubrication

This article presents the analysis of a two-lobe hole-entry hybrid journal bearing operating with micropolar lubrication. The modified Reynolds equation governing the laminar flow of isoviscous, incompressible micropolar lubricant in the clearance space of a journal bearing system has been solved using a finite element model incorporating appropriate boundary conditions. A comparative analysis between circular and noncircular two-lobe hybrid journal bearings with capillary restrictor under Newtonian and micropolar lubrication has been presented. It is concluded that bearing performance characteristics are significantly influenced by micropolar lubrication.     

Thermohydrodynamic Analysis of a Journal Bearing in a Turbulent Flow Regime—Part II: Application to an Axial Groove Bearing

The governing equations developed in (1), where a perturbation method is applied in the equation of motion and the energy equation is linearized, are used to study journal bearings of finite length operating in turbulent flow regimes. The thermohydrodynamic solutions are obtained for a journal bearing with four axial grooves. Heshmat and Pinkus' mixing theory (2) is used to evaluate the inlet temperature of each sector. These governing equations are solved to yield pressure, mass-mean velocity and temperature distributions, the mixing temperature at the inlet and the flow rates at the entry and exit of each sector, and the fictional forces.