Performance Characteristics of Worn Journal Bearings in Both Laminar and Turbulent Regimes. Part I: Steady-State Characteristics

The effects of geometric change due to wear on the hydrodynamic lubrication of journal bearings are determined theoretically and experimentally in both laminar and turbulent regimes. The steady-state characteristics of the bearings such as film pressure, attitude angle, and Sommerfeld number are analyzed by a semianalytical finite element method for various wear depth parameters, and the theoretical results are compared with the experimental results.

It is found that the geometric change due to wear has significant effects on the steady-state characteristics in both laminar and turbulent regimes. Good agreement is obtained between the theoretical and experimental results.     

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.     

On Performance Characteristics of Three-Lobe Porous Hydrodynamic Journal Bearings

This paper presents an analysis of a three-lobe porous hydrodynamic journal bearing for its static and dynamic performance characteristics. The performance characteristics of the bearing have been computed and presented in graphical form for a wide range of permeability parameter to investigate the effect of porosity on bearing performance. The stability margin of the three-lobe journal bearing system, in terms of crtical mass of journal, has been established using Routh's criteria. The nature of transient motion of the journal has been analyzed using the complex eigen values of characteristic equation and motion trajectories obtained by numerical integration of equations of motion.     

混合轴承动特性简化计算方法

用一维流计算原理分析了多腔混合轴承的动态特性；计算了典型的毛细管节流四腔轴承在各种设计参数下的线性化刚度系数和阻尼系数，得到了轴承相应的刚度和稳定性速度阈值；比较了简化计算方法得到的数据与传统的雷诺方程数值解法得到的数据，且讨论了前者的误差影响。在常用工况条件下，其计算结果满足工程需要。     

热膨胀对自密封滑动轴承润滑液泄漏的影响分析

本文以支承HDD主轴的自密封滑动轴承为对象,通过一个简化模型研究了因热膨胀导致的润滑液泄漏问题。分析表明,轴承的存油空间（包括间隙、油孔、油槽等）的容积膨胀率αT与润滑液的体膨胀系数αoil不匹配是造成温度变化时润滑液泄漏的重要原因。为减少泄漏,一方面应选用低膨胀液体作为润滑剂,另一方面应通过轴承设计以控制存油空间的膨胀率。控制αT的措施包括：（1）以线膨胀系数不同的材料制作滑动轴承摩擦副的不同零件（如轴套和外圈）;（2）根据轴承尺寸及材料、润滑液类型确定适当的轴承间隙比;（3）尽可能减少不油孔、油槽等除轴承间隙之外的存油空间。     

On the Dynamics of Lubricated Cylindrical Roller Bearings,Part I: Evaluation of Stiffness and Damping Characteristics

The stiffness and damping coefficients of a single roller-to-race contact of lubricated cylindrical roller bearings are numerically evaluated using a linearized perturbation method for both elastohydrodynamic lubrication (EHL) finite and infinite contact theories. A steady-state pressure equation is solved by a multilevel method and the elastic deformation is evaluated with the multilevel multi-integration method. Dynamic pressures are obtained by solving a set of perturbed pressure equations and are used to calculate the stiffness and damping coefficients. The influence of various nondimensional parameters (load parameter, speed parameter, material parameter, edge radius, and geometrical parameter) on the stiffness and damping are studied. The results show that a finite line contact gives higher values of stiffness and damping coefficients compared to an infinite contact, particularly at higher load and lower speed values. Based on the numerically evaluated data, curve-fitted relations for the stiffness and damping coefficients of a single roller-to-race contact are developed that can be used in the dynamic analysis of rotor–bearing systems.     

On the Dynamics of Lubricated Cylindrical Roller Bearings,Part II: Linear and Nonlinear Vibration Analysis

This article is the second part of two companion papers. In the first article, curve-fitted relations of stiffness and damping coefficients of a single roller-to-race contact of lubricated roller bearings were developed. In the present work, these relations are applied to a rotor–bearing system. Two cases are studied to investigate the influence of lubricated cylindrical roller bearings on the vibration characteristics of the rotor system. In the first case, lubricated contacts are simulated as a linear spring–damper model. The overall stiffness and damping matrices are calculated by using the dynamic coefficients of individual load sharing rollers. These matrices are used in the finite element analysis of flexible rotor. In the second case, the nonlinear structural vibration of a lubricated cylindrical roller bearing is studied. Equations of motion of bearing elements are derived using the Lagrange equation. A nonlinear load–deflection contact model developed through the derived curve-fitted relations of dynamic coefficients is used in the equations of motion. Equations of motion are solved by a fourth-order Runge-Kutta integration method. The response of bearing elements under free vibration and due to rotating unbalance is studied for damped and undamped cases. Furthermore, results obtained using elastohydrodynamic finite and infinite contact theories are compared.     

Improvement in Dynamic Characteristics of Circular Journal Bearings by Means of Longitudinal Microgrooves

Longitudinal microgrooves were assumed on the circular journal bearings and static and dynamic characteristics were investigated by solving the modified Reynolds equation for a rough bearing surface. It was found that the dynamic characteristics of the journal bearings were improved by longitudinal microgrooves or truncated micro-grooves on the bearing surface while the static characteristics, such as load-carrying capacity and friction coefficients, were not changed by the microgrooves. Calculations regarding the linear stability of a symmetrical rotor supported by two journal bearings were also carried out and it was found that the stable region was expanded on the stability chart by microgrooves.     

Exploring Operation Mechanisms of the Flexible Metal-to-Metal Face Seal: Part I—Numerical Modeling and Validations

A numerical model was developed for a special type of metal-to-metal face seal to evaluate its performance under various operating conditions. The model considers interactions among surface deformations due to thermomechanical twists, oil transport in the sealing band, and heat transfer in the seal pair simultaneously. In the meantime, experimental efforts have been made to measure the friction coefficients and seal temperatures during different operations. The model predictions were then compared with the experiment results through the two above-mentioned quantities. The comparisons show that the numerical simulations consistently overestimate the friction by 15–20%. However, the overall trend of friction variation with speed and some details of the friction have been captured, indicating that the current models are able to properly predict tribology of seal operations.     

Elastohydrodynamically Lubricated Ball Bearings with Couple-Stress Fluids,Part II: Dynamic Analysis and Application

Stiffness and damping coefficients of isothermal elastohydrodynamically lubricated point-contact problems are evaluated numerically with couple-stress fluids. A set of equations under steady-state and dynamic conditions is derived from the modified Reynolds equation using a linearized perturbation method. This paper is the second part of the present study; the modified Reynolds equation derived from the Stokes micro-continuum theory is used in the previous article. Dynamic pressures are found after solving the set of perturbed equations using the previously obtained steady-state pressure from the modified Reynolds equation. The stiffness and damping coefficients of the film are determined using the dynamic pressures. Then the overall stiffness and damping matrices of the ball bearing are obtained from load distribution, coordinate transformation, and compatibility relations. The bearing coefficients are introduced into a rotor system to simulate the response. It has been observed that the influence of couple-stress fluids on the dynamics of a rotor supported on lubricated ball bearings is marginal; hence, Newtonian theory can be used instead for simplicity. However, with increasing content of polymer additives in lubricant, for an accurate analysis the effect of couple stresses in a fluid should not be neglected.     

Lubrication Analysis of a Connecting-Rod Bearing in a High-Speed Engine. Part II: Lubrication Performance Evaluation for Non-Circular Bearings

In this article a numerical investigation of a connecting rod bearing operating at 6,500 rpm is performed. This is a companion to an earlier article that took into account the effects of the inertial force and the variable bolt tension force, which are considered to be the principal factors that affect the connecting rod bearing lubrication characteristics of an engine running at high speed. It was found that a thinner minimum oil film and a larger peak hydrodynamic pressure are predicted in a deformed connecting rod bearing than in a rigid connecting rod bearing. Multi-peaked hydrodynamic pressure was found to appear as well because of two or more converging-diverging film regions.     

Properties and Performance of Gas-Expanded Lubricants in Tilting Pad Journal Bearings

Lubricants enable proper function and reduce friction in rotating machinery, but they can also contribute to power loss and heat buildup. Gas-expanded lubricants (GELs) have been proposed as tunable mixtures of lubricant and CO₂ under pressure with properties such as viscosity that can be controlled directly in response to changing environmental or rotordynamic conditions. In this work, experimental results of GEL viscosity, gas diffusivity, and thermal conductivity were combined with high-pressure phase equilibrium data to understand how these mixtures will behave in tilting pad journal bearings under a range of industry-relevant high-speed conditions. Simulations were carried out using the experimental data as inputs to a thermoelastohydrodynamic model of tilting pad journal bearing performance. Viscosity could be easily tuned by controlling the composition of the GEL and the effect on bearing efficiency was appreciable, with 14–46% improvements in power loss. This trend held for a range of lubricant chemistries with polyalkylene glycols, polyalpha olefins, and a polyol ester tested in this work. Diffusivity, which drives how readily CO₂ and lubricants form homogenous mixtures, was found to be a function of the viscosity of the synthetic lubricant, with more viscous lubricants having a lower diffusivity than less viscous formulations. Model results for a bearing in a pressurized housing suggested that cavitation would be minimal for a range of speed conditions. Other bearing parameters, such as eccentricity, temperature, and minimum film thickness were relatively unchanged between conventionally lubricated and GEL-lubricated bearings, suggesting that the efficiency improvements could be achieved with few performance tradeoffs.     

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.     

Effect of Lubricant Non-Newtonian Behavior and Elastic Deformation on the Dynamic Performance of Finite Journal Plastic Bearings

This paper presents a numerical study of the performance of a dynamically loaded finite journal plastic bearing lubricated with a non-Newtonian fluid, taking into account the elastic deformation of the bearing. The non-Newtonian characteristics are adopted in this paper through an equivalent power-law. An expression for a modified Reynolds equation is derived in order to obtain the pressure gradient. Elastic deformation of the bearing surface was estimated in a direction normal to the bearing surface using Boussinesq equations. The film shape was modified accordingly and then iterated with the hydrodynamic pressure distribution in the bearing until a convergent solution was obtained. The Reynolds equation was solved numerically, considering three values of the flow-behavior index (n = 0.6, 1, and 1.2) and a wide range of journal speeds, materials, and clearance ratios. Consequently, the finite perturbation technique was used to determine the eight values of oil film stiffness and damping coefficients. By using the dynamic coefficients, the stability characteristics of the rotor-bearing system and the critical speed were calculated. The results show that increasing the flow-behavior index enhances the rotor-bearing system stability. A considerable destabilizing effect is obtained upon decreasing the elastic deformation coefficient.     

Numerical Study of the Sensitivity of Tilting-Pad Journal Bearing Performance Characteristics to Manufacturing Tolerances: Dynamic Analysis

In engineering practice, the predictions of bearing steady state and the dynamic characteristics are based on the bearing nominal dimensions. However, as the authors showed in a previous study (Fillon, et al. (1) Fillon, M., Dmochowski, W. and Dadouche, A. 2007. Sensitivity of Tilting Pad Journal Bearing Performance Characteristics to Manufacturing Tolerances. Trib. Transactions, 50: 387–400. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), manufacturing tolerances related to the bearing geometry (e.g., bearing clearances or angular pivot position) can significantly affect the steady-state characteristics such as the operating temperature, the minimum film thickness, and the power loss. This paper investigates changes to the bearing dynamic properties due to variations of the design parameters within the manufacturing tolerances. The dynamic properties of the tilting-pad journal bearings are represented by eight linear coefficients of stiffness and damping.

The study presents results obtained for realistic variations of bearing clearance, preload, pivot offset, as well as the pad angular extension. As an example, five-pad tilting-pad journal bearings with a diameter of 76.2 mm (3 in.) and three different L/d ratios have been used.     

An Original Definition of the Profile of Compliant Foil Journal Gas Bearings: Static and Dynamic Analysis

This article deals with a numerical analysis of the static and dynamic performance of a compliant journal gas bearing. The common approach found in foil bearing literature consists in calculating the carrying capacity for a given shaft position. In this study the external load is fixed (magnitude and direction) and the related shaft position is investigated. Nevertheless, a rigid profile, able to support high imposed loads, is no longer valid if one considers that the bearing becomes compliant. An original calculation method of the initial profile considering rigid surfaces is proposed to overcome this problem. The prediction of nonlinear dynamic behavior, i.e., stability and response to external excitation, is investigated. Finally, a viscous damping model is introduced into the dynamic model in order to obtain the amount of structural damping necessary to increase the stability of the compliant journal gas bearing.     

Dynamic performance of integral buckle arrestors for offshore pipelines. Part II: Analysis

A design methodology for integral buckle arrestors for deepwater pipelines was presented in a previous study (Park TD, and Kyriakides S., International Journal of Mechanical Sciences 1997;39:643–69). It was based on experiments and analyses in which buckles engaged the arrestors quasi-statically. In this two-part paper series, the performance of the same arrestors is reevaluated under the more realistic dynamic buckle propagation conditions encountered in the sea. The experimental program described in Part I involves tubes with D/t=27.9 and arrestors with L_a /D=0.5. The quasi-static arresting efficiency of buckle arrestors is first established experimentally as a function of the arrestor thickness. The same arrestor designs are then tested again in constant pressure environments where buckles propagate at velocities of 400–1100 ft/s. Experiments are conducted using both water and air as pressurizing media. A typical test specimen involves a relatively long upstream section of tube welded to an arrestor and to a downstream tube. The buckle is initiated in the upstream tube, accelerates to steady-state propagation, engages the arrestor and is either arrested or crosses over. For each arrestor design several such tests are required in order to bracket the dynamic crossover pressure. For all cases considered, the dynamic crossover pressure was found to exceed the corresponding quasi-static value. The reasons for this enhancement in performance are discussed in Part II in the light of results from numerical simulations of this process.     

基于多体动力学的发动机主轴承润滑特性Kriging建模

基于多体动力学(MBD)和弹性流体动力学(EHD)对某汽油发动机主轴承的润滑特性进行研究,利用实验设计(DOE)方法分析了半径间隙、轴承宽度、机油粘度和供油压力等设计变量对主轴承润滑性能,如最小油膜厚度(MOFT)、峰值油膜压力(POFP)、液动摩擦损失(FRIC)和机油端泄流量(Flow)等的影响,并利用Kriging方法建立准确表征主轴承润滑特性的简化模型。结果表明,Kriging可以在较少采样点的情况下建立较准确的主轴承模型。Kriging方法建立的简化模型计算和原始轴承仿真模型相比计算时间大大减少,可用于对轴承的设计优化。     

Dynamic analysis and grinding tracks in the magnetic fluid grinding system: Part II. The imperfection and ball interaction effects

To model the effects of the geometrical imperfections on the ball motion and its grinding track, it is therefore necessary to combine a dynamic model of the support system of balls with the previous model. For the geometrical imperfections on the ball, because of the interaction between the contact loads and the ball-spin speed, it causes the friction contact condition to remain at the interfaces with lower contact loads and lower ball-spin speeds in the separation case at the initial stage. Consequently, the variation in the ball-spin angle and the area covered by the grinding tracks is small. However, when the intermittent separation occurs at the geometrical imperfections on the ball orbit, it causes a large oscillation in the ball-spin angle and the ball-spin speed. Consequently, the effect of the imperfections in the ball orbit on the area covered by the grinding tracks is larger than that of the ball geometry. Ball–ball contacts cause a large oscillation in the ball-spin angle resulting in a uniform distribution of the grinding tracks. Hence, the effect of ball–ball contacts is one of the most important mechanisms in achieving a uniform distribution of the grinding tracks.     

Rolling cylinder on an elastic half-plane with harmonic oscillations in normal force and rotational speed. Part I: Solution of the partial slip contact problem

We study the effect of harmonic oscillations during the steady rolling of a cylinder on a plane in partial slip contact conditions in the limit of small oscillations. The solution is an extension of that given in Barber et al. [1] for infinitely large coefficient of friction. Here, the effect of varying normal load and hence contact area is investigated in detail by analyzing the first order variation of the tangential force and the corresponding relative displacements.In particular, the solution is given in terms of an explicit length scale d in the Flamant solution used as a Green function. Appropriate choice of values of d allows to treat both two-dimensional problems and three-dimensional ones having elliptical contact area sufficiently elongated in the direction of the rotation axis.Also, this analysis can be used as starting point for corrugation calculations in railway tracks, where oscillations in time of the normal forces can result in non-uniform wear and hence in amplification of the corrugation.