Thermohydrodynamic Behavior of Misaligned Plain Journal Bearings: Theoretical and Experimental Approaches

Hydrodynamic journal bearings are essential components for supporting and guiding the rotating shafts of high-speed machinery. Manufacturing defects in assembly or thermal distortions may introduce problems during running, such as misalignment. The destructive effects of this kind of running problem have justified the development of a numerical model to predict the bearing operating characteristics under steady-state conditions. The present work presents in detail the three-dimensional thermohydrodynamic approach adopted in this study in order to consider the thermal field variations. This model also includes lubricant film rupture and reformation phenomena by conserving the mass flow rate. In addition, an experimental validation is made by comparison with measurements carried out on our test device for various operating conditions and misalignment torques. The influence of misalignment direction is also investigated by considering numerical and experimental approaches used in the study of bearing behavior variations.     

Dynamic Behavior of an Unbalanced Rotor on Lubricated Bearings

In this paper the dynamic behavior of an unbalanced rotor on journal bearings is experimentally investigated. The static unbalance values are obtained by two adjustable rings. Tests are performed for a variety of lubricant flow rates, static unbalance values, ratios of bearing length-to-diameter and lubricant viscosities.

The results of this study show that, from a qualitative point of view, there is good agreement with the theoretical predictions made by Lund and Nielsen, in particular for a bearing with an L/D = 1. However, it is shown that the oil flow rate greatly affects the dynamic behavior; this aspect is not adequately considered in previous theoretical investigations.     

On the Adjusting of the Dynamic Coefficients of Tilting-Pad Journal Bearings

This paper gives a theoretical and experimental contribution to the problem of active modification of the dynamic coefficients of tilting-pad journal bearings, aiming to increase the damping and stability of rotating systems. The theoretical studies for the calculation of the bearing coefficients are based on the fluid dynamics, specifically on the Reynolds equation, on the dynamics of multibody systems and on some concepts of the hydraulics. The experiments are carried out by means of a test rig specially designed for this investigation. The four pads of such a bearing are mounted on four flexible hydraulic chambers which are connected to a proportional valve. The chamber pressures are changed by means of the proportional valve, resulting in a displacement of the pads and a modification of the bearing gap. By changing the gap, one can adjust the dynamic coefficients of the bearing. With help of an experimental procedure for identifying the bearing coefficients, theoretical and experimental results are compared and discussed. The advantages and the limitation of such hydrodynamic bearings in their controllable form are evaluated with regard to application on the high-speed machines.     

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.     

Influence of Surface Geometry on the Hydrodynamic Performances of Parallel Bearings in Transient Flow Conditions

Because a perfectly smooth surface does not actually exist, the classical principles of fluid mechanics dictate that the flow between two surfaces that are in relative motion is fundamentally unsteady. Therefore, the fluid film profile can be submitted to rapid oscillations in both space and time. This article shows how these oscillations become dependent on the surface geometry. By employing a transient mass-conserving cavitation model, we study several cases in which surface roughness and surface texturing are considered on both surfaces of a parallel bearing. For an applied load, the model shows the impact of surface geometry on the hydrodynamic performance of the bearing in terms of nominal film thickness, friction force, and volumetric flow rate. In addition, the results illustrate how different operating parameters such as the applied load and the speed of the moving surface affect the presence of cavitation within the bearing.     

滑动轴承油膜参数识别及稳定性研究综述

文章介绍在转子-滑动轴承油膜参数识别和稳定性分析领域所做的研究工作，以及现代知识在这一领域内所遗留下来的空白。简述了识别方法，提出了进一步研究的理论依据和实验基础，最后，作者指出本研究在相关领域中的地位、作用和意义，阐述了作者的观点。     

The Effect of Material Variables on the Fatigue Life of AISI 52100 Steel Ball Bearings

The effect of material variables on the fatigue life of AISI 52100 steel in ball bearings is examined. An apparently significant negative correlation with the abundance of certain trace alloying elements has been found. An effect of gas content has not been proven. Some difference in the endurance of bearings tempered for various lengths of time at different temperatures is shown. The most effective means available for obtaining improved fatigue life are certain techniques of vacuum melting. An approximate two-fold increase over catalog fatigue life is obtained by single vacuum melting, and a 7.7-fold increase has been achieved in tests using multiple consumable electrode vacuum remelting. This, in conjunction with previously reported evidence for the existence of a lower limit for fatigue life, suggests the possibility of producing bearings with better than 99.5% reliability at catalog life.     

高速紊流液体动静压混合轴承理论分析

通过考虑紊流、空穴以及润滑剂的惯性，可压缩性的影响，结合高速主轴轴承设计实例，提出了高速液体动静压混合轴承较全面的数学模型及设计计算过程，并对数值计算结果进行了分析讨论。     

Observation and Prediction of Cavities in a Lubricant Between Non-Parallel Disks in Relative Rotation

Observed and predicted cavity shapes in a lubricant between two disks are presented. The geometry is similar to that of a thrust bearing or a face seal having non-parallel rotating surfaces. Photographs of cavitated regions are shown and compared with predictions of cavity shapes obtained by an approximate calculation method analogous to the short bearing analysis used for journal bearings. The calculation and the experiment show steady state cavities that are symmetric about the maximum gap thickness. For small angles of disk inclination a single exterior cavity is seen and for larger values of inclination both an interior and an exterior cavity are present. The predicted cavity shape in a given case is a function of the disk inclination, the lower bound pressure for the oil film and rotor speed. General agreement on the cavity shape is obtained between theory and experiment.     

滑动轴承两种油膜边界条件的比较

本文对滑动轴承计算中两种常用的油膜边界条件进行了比较，一种是雷诺边界条件，另一种即质量守恒边界条件。对于前者，常采用负压力归零法进行计算，对于后者，大多采用Elrod算法。本文通过改变Elrod算法中的变量θ的定义，对Elrood算法进行改进，建立一新的通用方程，可自动确定动态边界，并在稳态工况下，将两种边界条件的计算结果与实验数据进行比较，发现根据质量守恒边界条件采用本文新改进的算法计算所得结果与实验数据十分吻合，同时，计算结果表明，空穴并不总是降低轴承的承载力，在稳态工况下，当空穴压力为较大的负压力时，轴承的承载能力反而有明显提高。     

The Effect of Perturbation Amplitudes on Eight Force Coefficients of Journal Bearings

This paper investigates the relationship between eight linear oil-film force coefficients of circular journal bearings and the perturbation amplitudes. The force coefficients are calculated by the finite perturbation method and compared with those calculated by the infinitesimal perturbation method. Numerical experiments show that the calculated results from both finite perturbation and infinitesimal perturbation methods are very close (with a variation less than 0.1 %) when the perturbation amplitudes are less than 0.02c (displacement) or 0.02ωc (velocity) for normal bearing eccentricities. For eccentricities between 0.2 and 0.8, the calculated coefficients by the finite perturbation method will differ less than 2.5 % from the results by the infinitesimal perturbation method if the perturbation amplitude is less than 0.05c or 0.04ωc. The bearing coefficients calculated by the finite perturbation method under different perturbation amplitudes are presented graphically.     

Experimental Determination of the Dynamic Characteristics of a Two-Axial Groove Journal Bearing

A hydrodynamic bearing test rig was used to experimentally study the steady operating characteristics and dynamic coefficient of a plain two-axial groove journal bearing. Using two electrodynamic shakers to generate synchronous sinusoidal excitations, two small independent elliptical displacement orbits were produced for different static equilibrium positions. Data was measured for two fixed shaft speeds, while the steady load was varied to achieve Sommerfeld numbers ranging from 0.063 to 0.344. The four linearized stiffness and four linearized damping coefficients were determined for each speed-load condition by reducing the orbital data using an average magnitude and phase method. The coefficients are presented in dimensionless form as functions of the Sommerfeld number. Typical average uncertainty was found to be 12 percent for the coefficients and 8 percent for the Sommelfeld number. For the speed, load, and temperature ranges tested herein, the dynamic coefficient results for each speed agreed within the uncertainty of the data, supporting the first order approximation that, for the operating range studied, a coefficient's magnitude is independent of the absolute speed, load, and viscosity so long as the Sommerfeld number is matched. The same conclusion was reached for the steady operating location within the bearing clearance space. The overall consistency of these results also lends confidence as to their reliability. Additional experimental results presented include three sets of continuous circumferential oil film thickness and pressure profiles, and discrete temperatures.     

Severity Estimation of Cracked Shaft Vibrations within Fluid Film Bearings

The equations of motion, with four degrees of freedom, taking into consideration the flexibility, damping and cross coupling of the fluid film bearings are derived for a cracked Jeffcott rotor supported on fluid film bearings.

Dimensionless equations are developed for dynamic radial load, dynamic pressure developed in the fluid film bearings and coefficient of dissipation considering the journal vibrations in two harmonics; bearing fluid film stiffness and damping coefficients. These are applied to a cracked Jeffcott rotor supported on different types of bearings, i.e., cylindrical journal bearings, offset cylindrical bearings, tilting pad journal bearings and three-lobe bearings. Based on the allowable dynamic pressure developed in the fluid bearings, the severity of cracked shaft and allowable crack depths are estimated in this study. Measurement of dynamic pressure and dissipation for monitoring the crack growth is suggested. However, 2x vibration is the best indicator of cracks in the shafts.     

An Analysis of the Ga/In/WSe2 Lubricant Compact

Chemical analytical instrumentation and advanced surface analysis techniques were combined with X-ray diffraction to investigate the chemistry and the crystal structure of the well-known Ga/In/WSe₂ self-lubricating compact. The data indicate that the active ingredients within the compact are the lamellar gallium and indium selenides formed during the cure of this material. These solid lubricants work in conjunction with the residual WSe₂ not yet reduced by the Ga/In during the cure cycle. The binder encapsulant holding the lubricative entities together is the residual Ga/In eutectic, partially reacted to substoichiometric selenides of mostly indium. The high-temperature, tribooxidative resistance of the compact is attributed to a protective mechanism, whereby the substoichiometric indium selenides preferentially oxidize. The oxide network becomes a diffusion shield to the encapsulated, lamellar ingredients. The practical use of the compact is limited by inherent thermodynamic instability problem at elevated temperatures, and the removal of the protective oxide layers by tribological action.     

Thermoelastohydrodynamic Analysis of Fixed Geometry Thrust Bearings Including Runner Deformation

A thermoelastohydrodynamic theory for the analysis of sector thrust bearings is presented. The analysis includes the generalized Reynolds equation and a fully elliptic three-dimensional energy equation in the film. In addition, full three-dimensional heat transfer is allowed in the pad while axisymmetric conduction is allowed in the runner. Three-dimensional elastic deformation due to mechanical and thermal loading is allowed in the pad while axisymmetric mechanical elasticity is allowed in the runner. The performance of a parallel tapered-land thrust bearing including runner deformation effects is analyzed as a function of different models. It is seen that mechanical deformation of the pad affects the operating characteristics only slightly while thermal deformation of the pad can cause large increases in operating temperature. The runner deformation effects can include a reduction of the maximum film temperature at slight deformation or a large increase in film temperature at the inner radius of the pad at larger deformations.     

Linear Stability Analysis of Hydrodynamic Journal Bearings with a Flexible Liner and Micropolar Lubrication

A linear stability analysis of hydrodynamic journal bearings is presented, including the effects of elastic distortion of the liner and micropolar lubrication. Hydrodynamic equations of the lubricant and equations of motion of the journal are solved simultaneously with the deformation equations for the bearing surface to predict the fluid film pressure distributions theoretically. The components of stiffness and damping coefficients, critical mass parameter, and whirl ratio, which reflect the dynamic characteristic of the journal bearing, are calculated for varying eccentricity ratio taking into account the flexibility of the liner and the micropolar properties of the lubricant. The results presented show that stability decreases with an increase in the value of the elasticity parameter of the bearing liner and micropolar fluids exhibit better stability in comparison to Newtonian fluids.     

轴承弹性变形对动载滑动轴承润滑状况影响的分析

本文讨论了等温弹性流体动力润滑方程的求解方法和动载滑动轴承弹性变形对润滑油膜的影响，分析表明该方法是求取轴心轨迹和对轴承润滑状况预测的较合理方法。     

温度及压力对滑动轴承气蚀磨损影响的实验研究

采用超声振动原理建立了滑动轴承模拟气蚀实验装置 ,研究了温度及压力变化对滑动轴承气蚀磨损的影响。发现温度及压力的升高都会使滑动轴承的气蚀磨损增加。并对这一现象从理论上进行了分析     

An Investigation of the Steady-State Performance of a Pivoted Shoe Journal Bearing with ISO VG 32 and VG 68 Oils

This article presents a report on an investigation into the performance characteristics of a steadily loaded pivoted shoe journal (PSJ) bearing that is lubricated with ISO VG 32 and VG 68 oils. The article describes a testing machine on which the experimental investigation was performed. Measurements of shaft torque, pad temperature distributions, oil inlet and outlet temperatures, oil flow rate, and eccentricity have all been recorded as functions of load and speed. The experimental results from both test oils are presented in graphical form and are compared with theoretical predictions obtained from the author's computer model of the PSJ bearing. These results showed that the thicker ISO VG 68 oil provided thicker oil films. However, it also had higher bearing temperatures and power losses. A good correlation between the theoretical and experimental results has been found. Theoretical analysis of the bearing friction losses indicate that shear losses predominate and churning losses account for approximately 20% of the total losses.     

Non-Linear Transient Stability Analysis of a Rigid Rotor Supported on Hydrodynamic Journal Bearings with Rough Surfaces

Non-linear transient stability analysis has been performed to study the sub-synchronous whirl stability of a rigid rotor supported on two symmetric hydrodynamic bearings with rough surfaces subjected to a unidirectional constant load. A Reynolds type equation for finite hydrodynamic bearings, with different models of rough surfaces, has been solved using the stochastic finite element method. The trajectories of the journal center have been obtained by solving the equations of motion of the journal center by the fourth-order Runge-Kutta method. Results show an increase in the stability with transverse roughness and a decrease in the stability with isotropic roughness. A small improvement in stability is obtained with longitudinal roughness.