Lubrication Analysis of a Connecting-Rod Bearing in a High-Speed Engine. Part I: Rod and Bearing Deformation

Analysis was performed on a connecting rod assembly operating at 6,500 rpm. The analysis was based on the finite element method, which includes effects of interference fitted bearings and pre-loaded bolts. The rod inertia force associated with the gas pressure was found to have a significant effect on the variation of the rod bearing shape. The shape variation of a connecting rod assembly is commonly ignored in rod bearing analyses. Investigation of bearing deformation was conducted in order to evaluate the lubrication characteristics.     

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.     

弹性变形对径向轴承弹流润滑性能的影响

本文以上具有不同弹性模量、泊松系数的两种轴承材料为例分析了弹性变形对有限长径向滑动轴承的弹流润滑性能的影响。流体动力润滑方程采用雷诺方程,应用力学问题的通用有限元软件ＭＡＲＣ产生柔度矩阵计算弹性变形。对比分析了二种轴承的油膜压力分布、油膜厚度分布、最小油膜厚度以及承载能力。     

Elastohydrodynamically Lubricated Ball Bearings with Couple-Stress Fluids,Part I: Steady-State Analysis

Conventional elastohydrodynamic lubrication (EHL) analysis of point contacts is extended to include couple-stress effects in lubricants blended with polymer additives. A transient pressure differential equation, generally referred to as a modified Reynolds equation, is derived from the Stokes microcontinuum theory and solved using the finite difference method with a successive over-relaxation scheme. The solution is obtained under isothermal conditions, assuming a suitable exponential relation of pressure-viscosity variation. A nondimensional couple-stress parameter, which can be considered the molecular length of the additives in the lubricant, is used in the analysis. From the results obtained, the influence of the couple-stress parameter on the EHL point contacts is apparent and cannot be neglected. Lubricants with couple stresses provide an increase in the load-carrying capacity and reduction in friction coefficient as compared to Newtonian lubricants. Empirical formulas for the calculation of central and minimum film thicknesses of lubricated point contacts with couple-stress fluids are derived with the nonlinear least-squares curve-fitting technique using different numerically evaluated data. This may help to avoid the time-consuming numerical calculations.     

计入曲轴受载变形的粗糙表面曲轴轴承弹性流体动力润滑分析

对一四缸内燃机曲轴轴承进行了计入曲轴受载变形和表面形貌的弹性流体动力润滑分析.计算中采用动力学法进行曲轴轴承的润滑分析,采用变形矩阵法计算油膜压力作用下轴瓦表面的变形.结果表明,表面形貌对曲轴轴承轴心轨迹影响较大,表面弹性变形对曲轴轴承轴心轨迹影响很小;计入表面形貌,曲轴轴承最大油膜压力增大显著,最小油膜厚度明显减小,端泄流量在大部分时间几乎没有变化;计入表面弹性变形,轴承最大油膜压力基本都有不同程度的减小;表面弹性变形对端泄流量、轴颈摩擦因数以及最小油膜厚度的影响甚小.     

Analysis of High-Speed Cylindrical Roller Bearings Using a Full Elastohydrodynamic Lubrication Model Part 2: Results

The kinematic and dynamic characteristics of high-speed cylindrical roller bearings are analyzed using the elastohydrodynamic (EHD) lubrication model developed in Part I of this two-part paper. The internal load distribution, bearing stiffness, running torque, and amount of roller skidding are calculated under various operating conditions. Effects of manufacturing imperfections are also analyzed in terms of outer-raceway waviness and roller diameter tolerance. Results obtained through case studies indicate that the behavior of the bearing can be significantly affected by EHD lubrication in the roller-raceway contacts.     

高功率密度柴油机连杆大头轴承润滑特性分析

基于全局 Newton-Raphaon 方法和柔度矩阵法对高功率密度柴油机连杆大头轴承的润滑性能进行数值摸拟;耦合求解 Reynolds 方程和弹性变形方程,比较弹性变形的连杆大头轴承与刚性轴承的轴心轨迹与压力分布。结果表明：将全局 Newton-Raphaon 方法与柔度矩阵法结合起来,对高功率密度内燃机连杆大头轴承的弹流润滑进行分析,解决了轴承偏心率大于1时弹流润滑计算难于收敛的问题;考虑表面弹性变形的连杆大头轴承与刚性轴承相比,在最大气体爆发压力附近,油膜压力分布的形状和大小明显发生变化,特别是在轴承的两端处,油膜压力明显增加并接近轴承中间部分的压力。     

Measurement of Cage and Pocket Friction in a Ball Bearing for Use in a Simulation Program

Few measurements have ever been made of the drag forces arising in a ball bearing due to viscous friction of the balls rotating in the cage pockets and the cage rotating inside the raceway. This paper reports measurements of both these sources of friction on simulations of just one bearing, but the data are compared with general analytical expressions for predicting the friction, and agreement is good. Finally, the data for the ball/pocket friction are compared against a theoretical model based on simple viscous shear and are shown to be in excellent agreement.     

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.     

A Study of Dynamically Loaded Finite Journal Bearings in Mixed Lubrication Using a Transient Thermohydrodynamic Analysis

A transient analysis of dynamically loaded finite journal bearings in mixed lubrication is made by solving the modified generalized Reynolds equation, 2-D energy equation in the oil, and heat conduction equation in the journal simultaneously including mass conserving cavitation. ISOADI (isothermal shaft and adiabatic bushing inner surface) thermal boundary condition is used. Journal temperature is treated as quasi-steady over one loading cycle. Two kinds of contact model are used. Numerical solutions using the finite difference method are presented. Results shows that the bearing behavior is closely tied to the roughness texture and topography, asperity contact load, bearing geometry, and operating conditions.     

Flow Characteristics of Hydraulic Fluids of Different Viscosities II. Flow in Pumps: Internal Leakage and Loss of Efficiency

A new type of hydraulic fluid, the high-water type, is being developed for use in industrial equipment which is currently using oil or oil-like fluids. In order to determine which factors affect the flow properties of high-water hydraulic fluids, a series of solutions ranging in viscosity from that of a water-glycol fluid (55 mPa·s or 250 SUS) to that of a high-water fluid (3 mPa·s or 35 SUS) was formulated by varying the amount of thickening agent. From flow rates of these fluids at known pressure and viscosity, the efficiency (percent loss of flow) was calculated. As would be expected, internal leakage from the high-pressure side of the pump to the low-pressure side was much greater with the 3 mPa·s fluids than with the 50 mPa·s fluids. Increasing the pump size increased pump efficiency at a given viscosity.

Equations relating pressure, viscosity and flow for two types of internal leakage were developed by mathematical or graphical analysis of the experimental data.     

Transmission Electron Microscopy of Boundary-Lubricated Bearing Surfaces. Part II: Mineral Oil Lubricant with Sulfur-and Phosphorus-Containing Gear Oil Additives

Transmission electron microscopy (TEM) was performed on cross-sectional samples of tapered roller bearing cone surfaces that were tested at two levels of local boundary lubrication severity, Λ ～ 1.1 and 0.3. Unlike our previously reported work in which a base mineral oil was used, the bearing tests were conducted in mineral oil with sulfur- and phosphorus-containing gear oil additives. Structural and compositional characterization of undetached antiwear surface layers on the base steel (cone raceway) revealed that the films contained crystalline and amorphous regions. A sharp interface (<～10 nm) that separated the surface layer and base steel was imaged. The surface layer for the cone tested at Λ ～ 1.1 consisted of Fe, O, and P, whereas that for the cone tested at Λ ～ 0.3 consisted of Fe, O, P, C, Ca, and S. Various TEM analytical techniques were used to study the segregation of these elements throughout the antiwear surface layer volume.     

Transmission Electron Microscopy of Boundary-Lubricated Bearing Surfaces. Part I: Mineral Oil Lubricant

Transmission electron microscopy (TEM) was performed on the near-surface material (depth <500 nm) of tapered roller bearing inner rings (cones) that were tested at two levels of boundary-lubricated conditions in mineral oil with no additives. Site-specific thinning of cross section cone surface sections for TEM analyses was conducted using the focused ion beam (FIB) milling technique. High-resolution structural and compositional characterization of near-surface material and surface layers was performed on an untested cone as well as cones tested at Λ～1.1 and 0.3. This approach revealed near-surface microstructural distortion and grain size gradients that were attributed to surface finishing operations during manufacture. The characteristics of oxide surface layers and micro-cracks on the tested bearing surfaces were evaluated and found to depend on lubrication conditions.     

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.     

Theoretical Analysis of High-Speed Cylindrical Roller Bearing with Flexible Rings Mounted in a Squeeze Film Damper

For high-precision mechanical systems such as gas-turbine engines that operate under extreme conditions, it is particularly important to accurately predict the behavior of the mainshaft rolling bearings. This prediction includes, among others, the load distribution, stiffness, and power dissipation. Although the shaft speeds tends to increase, rings and shaft are becoming thinner due to size and weight constraints. Thus, the bearing behavior is now dependent on the housing and ring stiffness. Furthermore, the use of a squeeze film damper (SFD) is widespread in gas-turbine engines to significantly reduce the vibratory levels. In this case, a single thin ring provides the interface between the bearing rolling elements and the fluid film. Due to the flexibility of this ring, an elastic coupling occurs modifying the behavior of the bearing-SFD system. A global flexible bearing-SFD assembly model is proposed in this paper. Large deformations can occur, resulting in a contact between the ring common to the bearing and the SFD and its housing. To reproduce this interference, an effective mechanical stop model is also proposed. The behavior of an industrial bearing-SFD assembly is then investigated for different operating conditions. The presented results show that this coupling has a first-order influence on the behavior of the bearing-SFD system. It is also shown that such elastic coupling introduces a dissymmetry of the load distribution with respect to the applied load direction. Moreover, in certain cases, the position of the bearing in its housing can reach eccentricities larger than the radial clearance of the SFD.     

增压器浮环轴承润滑过程数值分析

以流体滑动轴承的润滑理论为基础,分析研究了内燃机增压器浮环轴承的工作机理和结构参数与性能的关系。建立了浮环轴承力平衡、力矩及摩擦功率损失的方程式,探讨了轴承内外膜承载能力与相应转速比、间隙比、偏心率等参数之间的关系。结果表明：浮动套内外半径比增大,偏心率减小,承载能力增大;间隙过大或过小,难以形成润滑油膜,影响承载能力;索氏数（Sommerfeld数）越大,则轴承的承载能力也越大。     

Performance Characteristics of Worn Journal Bearings in Both Laminar and Turbulent Regimes. Part II: Dynamic Characteristics

The effects of geometric change due to wear on the dynamic characteristics of journal bearings are determined theoretically in both laminar and turbulent regimes. The dynamic characteristics such as spring and damping coefficients and whirl onset speed of a rigid rotor supported by two identical symmetrically aligned bearings are analyzed by a semianalytical finite element method, and the numerical results for various wear depth parameters are indicated in graphical form.

The geometric change due to wear has significant effects on the principal spring coefficients and on the cross-coupled damping coefficients. The whirl onset speed for a worn journal bearing whose wear depth parameter is larger than 0.3 becomes higher than the speed for a nonworn bearing.     

Performance of a Complaint Foil Seal in a Small Gas Turbine Engine Simulator Employing a Hybrid Foil/Ball Bearing Support System

Operation of a non-contact compliant gas foil seal (CFS) in a high temperature hybrid dynamic simulator representative of a small gas turbine engine spool is discussed. At the hot section of the simulator two oil-free components, a CFS and a compliant foil bearing (CFB) were mounted and at the cold (compressor) section of the simulator, an oil-mist lubricated ball bearing was installed. The preliminary numerical study on the fluid flow and thermal analysis of a CFS was discussed in the previous work by the authors. The experimental results for successful operation of the foil bearing and foil seal at temperatures up to 560 °C and speeds up to 55,000 rpm are presented. The surface of the CFS and CFB journals for high temperature tests were coated with PS304 solid lubricant film, developed by NASA The CFS performance at different operating speeds and temperatures and differential pressures was investigated. In a similar test, a leakage flow comparison was made among a labyrinth seal, a brush seal and a CFS. The experimental results indicate superior performance of the CFS over the two other types of seals. Unlike brush seal, CFS showed no evidence of rub or induced wear on the journal or seal surface.     

A Chemical Kinetics Model to Predict Lubricant Performance in a Diesel Engine. Part I: Simulation Methodology

The ability of a lubricant to protect increasingly complex diesel engines directly affects engine durability and warranty costs and is becoming increasingly costly to validate. This paper presents a novel approach combining a chemical kinetic model using rate constants determined by a set of laboratory bench tests and a finite-difference computer program to predict lubricant performance in a given diesel engine. The computer program takes into account the engine's mechanical design, such as temperature, pressure, oil flow rate, top ring zone volume, and other parameters. The chemical kinetic model incorporates the kinetic rate constants determined for that particular lubricant in a set of special bench-test procedures tailored to a particular engine and its operating conditions. The bench-test procedures take into account the necessary environment in that particular engine such as specific metal catalysis, oxidation conditions, and deposit formation. The computer program then combines the lubricant degradation model with the engine operating sequence to yield a predictive simulation. This approach is capable of predicting the amount of deposit in the top ring groove and the amount of oil consumption in that engine. The computer program models the engine as three chemical reactors in series. The three reactors are: the oil sump, the top piston ring groove, and the piston cylinder-liner interface. Oil flows from the sump to the piston rings and to the piston liner area. The oxidation process is described by a set of simplified chemical kinetic rate equations. The kinetic constants of the lubricant are determined by laboratory bench-test procedures using Differential Scanning Calorimetry (DSC), a Thermal Gravimetric Analyzer (TGA), and the Micro-Oxidation test apparatus. The design and the operating conditions of the engine define the chemical reaction conditions used in the simulation program such as the temperatures of the reactions, the residence time in a particular reactor, the volume of the reactors, and the operating sequence of the engine. The simulation program is validated by the Caterpillar 1K engine dynamometer test results. Two experimental high-temperature lubricants and three IK reference oils were used in this study. Good agreement between model simulation and 1K engine test results was obtained.     

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.