Calculated Performance of Non-Newtonian Lubricants in Finite Width Journal Bearings

A numerical procedure has been developed for the calculation of the performance of non-Newtonian, polymer-thickened lubricants in finite width journal bearings. Such oils were found to act as if they had averaged “anisotropic viscosities,” i.e., different viscosities in the circumferential and side leakage directions, even though the viscosity was taken to have one definite value, a function of the resultant shear stress, at each point in the oil film. Overall, polymer oils carried less load at a given eccentricity, gave less friction and a flatter pressure distribution than mineral oils of the same low shear viscosities. By analogy with the previously calculated infinite width case, which gave similar results, it is expected that the flatter viscosity temperature slope of the polymer oils will compensate for their apparent viscosity decrease. The program has also been adapted to “natural” boundary conditions, which improve upon the delineation of the cavitation region on the inlet side of the 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.     

The Externally Pressurized,Porous Wall,Gas-Lubricated Journal Bearing.

The externally pressurized, gas-lubricated journal bearing consisting of a porous bushing, through which gas enters the clearance space, is analyzed. The classical Reynolds' equation for laminar, isothermal, compressible flow in a finite journal bearing is modified to allow for the local mass flow through the porous bushing into the clearance space due to the difference between the constant supply pressure and the pressure within the bearing. At low mass flow rates, it is assumed that the flow in the porous bushing obeys the Darcy equation for isothermal, compressible “creeping flow.” The analysis is extended to include bearings with higher flow rates by a simple modification of the Darcy equation.

The modified Reynolds' equation is solved for the case where the shaft does not rotate by perturbing the mass flow rate through the bearing using the eccentricity ratio as a small parameter. An asymptotic solution for the “short bearing” and the “maximum load-carrying capacity” is determined independent of the perturbation technique. The results of the perturbation technique are compared numerically with the results of the asymptotic solution, and they are found to be in agreement.     

An Evaluation of Starting-Load Capacity and Static Friction in Babbitt-Lined,Hydrodynamic Journal Bearings

A recent application called for starting 127-mm (5-in) diameter, babbitt-lined hydrodynamic journal bearings under unit loads of about 10.34 MPa (1500 psi). In this application, the load was imposed only a few seconds before rotation could be started and hydrostatic jacking was not permitted. This paper presents the results of a test effort in which one full-size bearing was subjected to several hundred starts under unit loads ranging from 3.4 to 15.5 MPa (500 to 2250 psi). The dwell time between load application and start of rotation was varied in the test from less than one second to more than one hour. The paper also provides a review of the relevant literature, as well as calculations of the contact zone temperature during starts under boundary lubrication conditions.     

Experimental Investigation of Whirl in Self-Acting Air-Lubricated Journal Bearings

Bearing characteristics influencing the threshold speed at which large-amplitude self-excited whirl occurs in complete, air-lubricated journal bearings were experimentally investigated. Various combinations of rotors having clearance ratios, Ψ = c/r, ranging from 0.268 × 10^?3 to 2.350 × 10^?3 and symmetrical bearing assemblies having slenderness ratios, L ′ = L/D, ranging from ¼ to 1 were tested.

By varying slenderness and clearance ratios and unit load, by opening or closing supply orifices, or by adding imbalance, the whirl threshold speed could be varied between zero and the limit set by the available power.

Experimental methods of identifying the cylindrical and conical modes of synchronous and self-excited whirl are described. The whirl hysteresis region and the nature of whirl at speeds above the threshold are examined. Three methods of avoiding large-amplitude self-excited whirl are discussed.     

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.     

不同润滑条件对塑料合金轴承摩擦磨损性能的影响

用MPV 2 0 0型摩擦磨损试验机对超高分子量聚乙烯 (UHMW PE)塑料合金轴承在水润滑介质不同含沙量的条件下进行了摩擦学性能测定 ,分别考察了载荷、速度以及运行时间等对合金轴承摩擦学性能的影响。为水润滑合金轴承的实际应用提供理论指导。     

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.     

材料弹性模量对滑动高副润滑性能的影响

本文通过理论分析和实验研究证明，降低滑动高副中材料的弹性模量，可显著地改善其润滑性能，易于实现全膜润滑。     

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.     

透平机小孔气体轴承性能的研究

利用有限元法求解稳态和摄动雷诺方程，对双排径向小孔静压气体轴颈轴承的静，动特性进行了分析。     

The Influence of Longitudinal and Transverse Profile on the Load Capacity of Pivoted Pad Bearings

An extension of previous work on the effects of surface profile on the load capacity of pivoted pad thrust bearings. Numerical solutions are presented for a square pad having profiles consisting of (a) longitudinal curvature, (b) transverse curvature, and (c) a combination of (a) and (b). Improved load capacity over the flat pad with optimum pivot location is found for some operating conditions including the case of the centrally pivoted pad.     

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.     

Calculation of Stribeck curves for line contacts

A mixed lubrication model is presented by which Stribeck curves can be calculated. By means of the Stribeck curve the transitions from boundary lubrication to mixed lubrication and the transitions from mixed lubrication to elasto-hydrodynamic lubrication can be predicted and subsequently the lubrication regime in which a particular contact operates can be predicted. Calculations are restricted to line contacts, because of the wide range of applications of line contacts or of very wide elliptical contacts.     

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.     

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.     

Friction Power Loss Simulation of Internal Combustion Engines Considering Mixed Lubricated Radial Slider,Axial Slider and Piston to Liner Contacts

Different types of mixed lubricated contacts are present in internal combustion engines. These are several radial slider bearings; for instance, in main bearings; big end, small end, and piston pin bearings; as well as axial slider bearings and piston–liner contacts. Phenomena such as friction power loss and wear as well as acoustic excitation and oil consumption of the overall lubrication system are mainly affected by these contacts. Therefore, the simulation-based investigation of oil film–lubricated contacts is important during the development process of internal combustion engines. Due to the highly nonlinear interactions, the applied mathematical models have to consider the dynamics of the overall flexible body system in addition to the detailed properties of the contacts and the lubricant itself.

This work outlines both the theory of the separated mathematical models and their coupling. The large number of nonlinear contacts, which is possible to consider when applying the presented coupling approach, is emphasized. Furthermore, application of a friction power loss analysis for an in-line four-cylinder internal combustion engine is described.     

Study of Influence of Helix Angle on Friction Characteristics of Helical Gears

The minimizing of friction loss of helical gears is one of today's most important problems. Though helical gears are very widely used in power transmissions of automobiles and ships, basic research on helical gears is comparatively scarce. Under these circumstances, the authors studied the friction loss of helical gears in view of various helix angles, loads, and rotational speeds. Further the relationship between temperature rise of teeth and friction loss was made clear. The results were discussed from the viewpoint of reduction of friction loss and were related to the results of the authors' spur gear tests. Friction loss and temperature rise of helical gear teeth were also investigated while the helix angles were widely varied. All these results, based on experimental investigations, were summarized and general formulas were established in view of gear design.     

On the Appearance of Lubricant Film Rupture in Cylindrical Journal Bearings

Based on energy and mass balances in conjunction with the classical Reynolds equation in the film region, expressions for cavitation phenomenon are developed. They determine the circumferential location angle where cavitation might start, and the potential number of bifurcating fluid streamer surfaces (boundaries between gas-liquid flow) can be estimated. The expressions depend on the journal angular velocity, equilibrium eccentricity ratio, and bearing and fluid characteristics; they strongly influence cavitation and have not been considered in previous studies. Conditions under which the cavitation phenomenon does not occur are also given. Finally, a comparison to previous research results showing a very close agreement is presented.     

稀薄效应对动压气体轴承静动特性的影响

为研究稀薄效应对微小间隙下动压气体轴承静动态特性的影响,分别采用连续模型、一阶滑移模型以及在任意克努森数下都与线性玻尔兹曼方程解有较高吻合的WU新滑移模型,基于有限体积法建立考虑稀薄效应的静动态Reynolds方程,给出3种模型下轴承静态承载力与偏心率、轴颈扰动频率与轴承动特性系数的变化关系。数值分析结果表明:随偏心率的变化,连续模型预测的静态承载力最大,一阶滑移次之,WU新滑移模型预测的值最小;随着扰动频率的增加,考虑滑移模型计算的主刚度系数和主阻尼系数均有减小的趋势,且WU新滑移模型计算的主刚度系数和主阻尼系数明显低于连续模型和传统的一阶滑移模型。传统连续模型和一阶滑移模型过高地估计了轴承的静动特性系数,WU新滑移模型计算的结果更为准确。