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.     

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.     

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.     

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.     

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.     

Stress Reversals in a Jeffcot Rotor Supported on Fluid Film Bearings

Under certain conditions a Jeffcot rotor supported on fluid film bearings can experience undesirable stress reversals at double the operating speed in synchronous whirl. When the damping in the hearings is not considered, the condition for complete stress reversal coincides with that for backward whirling of the disk. However, when the damping also is considered, the absolute whirl directions of the journal and the disk can be different under certain conditions. Hence, the rotor shaft may not experience backward whirl throughout its length. Under these circumstances, the relationship between complete stress reversal and backward whirling motion is ambiguous. The present investigation specifies the precise condition for complete stress reversal and identifies it with the relative backward whirling of the disk with respect to the journal.     

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.     

Hydrodynamic lubrication of porous journal bearings using a modified Brinkman-extended Darcy model

A numerical solution for the hydrodynamic lubrication of finite porous journal bearings considering the flexibility of the liner is introduced. The Brinkman-extended Darcy equations and the Stokes' equations are utilized to model the flow in the porous region and fluid film region, respectively. A stress jump boundary condition at the porous media/fluid film interface and effects of viscous shear are included into the lubrication analysis. Elrod's cavitation algorithm, which automatically predicts film rupture and reformation in the bearing, is implemented in the solution scheme. The present analysis predictions for pressure distributions, load carrying capacity, and friction factor are in good agreement with three different sets of experimental results available in the literature. Furthermore, the effects of dimensionless permeability parameter, and stress jump parameter on performance parameters such as load carrying capacity, side leakage, friction factor, and attitude angle, are presented and discussed.     

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.     

Effects of Excitation Frequency and Orbit Magnitude on the Dynamic Characteristics of a Highly Preloaded Three-Lobe Journal Bearing

The independent effects of excitation frequency and excitation magnitude on experimentally derived bearing coefficients for a highly preloaded three-lobe journal bearing were studied. The effect of excitation frequency was determined by applying external dynamic forces at half-synchronous, synchronous, and twice synchronous frequencies with respect to the operating speed. Effect of excitation magnitude was independently determined by applying either three or four different amplitudes of excitation force to the bearing resulting in orbit sizes ranging up to 30% of clearance. Applying static forces to the bearing housing controlled the Sommerfeld number, and thus, the static operating position. Data was reduced as linear dynamic coefficients, and presented relative to excitation frequency and excitation magnitude over a range of Sommerfeld numbers from 0.2 to 3.0 and operating eccentricities from 0.3 to 0.9. In general, neither excitation frequency nor excitation magnitude was shown to have a measurable effect over the ranges studied.     

Performance Experiments with a 200 mm,Offset Pivot Journal Pad Bearing

Journal bearings are an important design option, particularly appropriate for high-speed rotating machinery applications. This paper presents results from an extensive program of experimental work with a 200 mm, five-shoe, tilting-pad bearing of this type. The tilting pads were fitted with offset pivots; this is in contrast to most previous work which has concentrated on bearings with pads which have centrally mounted pivots. The new results obtained for the offset pivot pad bearing are compared with recently published, equivalent results for the same bearing filled with center pivot pads. A substantial temperature reduction in bearing temperature is revealed for the offset pivot case.     

Feasibility Study of Hydrodynamic Lubrication in Supporting of Rotating Elements of Galvanizing Hardware Submerged in Molten Zinc

Severe wear of sink roll supports in continuous galvanizing lines has been a cause for concern for some years. This wear, which affects the quality of the coating and downtime costs, is a result of a corrosive environment and highly loaded surface contact.

This paper presents results from a feasibility study to use journal bearings lubricated with molten zinc to separate the interacting surfaces. Analytical and experimental investigations were aimed at identifying the load capacity of sink roll bearings when operating in the hydrodynamic regime, as well as the effect of the molten zinc bath environment on bearing performance. This environment includes chemical zinc attack and the presence of inter-metallic particles in the bath.

The study indicates that it is difficult to achieve hydrodynamic bearing operation for the entire range of operating conditions. It also shows that, when selecting materials for journal bearings support to the rotating elements submerged in molten zinc baths, possible contact of the bearing surfaces as well as chemical inertness and resistance to the hard intermetallic particles do need to be addressed.     

Identifying Bearing Rotor-Dynamic Coefficients Using an Extended Kalman Filter

An extended Kalman filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates the cross-coupled damping coefficients were the least accurate.     

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.     

Non-Newtonian Effects of Powder-Lubricant Slurries in Hydrostatic and Squeeze-Film Bearings

This paper presents the result of pressure measurements made in hydrostatic and squeeze-film bearings lubricated with a powder-lubricant slurry. The powder lubricant was powdered graphite and the carrier fluid was ethylene glycol. Pressure measurements compared favorably with analytical predictions based on a power law rheological model.

The behavior of ethylene glycol acting alone as a lubricant was also analyzed to provide a baseline for comparing the effects of the graphite powder additive on pressure and flow rate.

The hydrostatic bearing test showed that the addition of graphite powder into ethylene glycol can raise the load-carrying capacity of a lubrication system however pumping requirements are also raised. Squeeze-film bearing tests showed that the damping factor is increased with the addition of powdered graphite into the carrier fluid.     

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.     

Steady-State and Transient Dynamic Simulation of a Continuous Foil Bearing

The objective of this paper is to present an integrated procedure which will analyze the dynamics of a foil hearing on elastic supports. A complete time-dependent Navier-Stokes formulation is used to solve for the interaction between the hydrodynamic effects of the fluid lubricant, the motion of the journal, and the deformable foil boundary. The elastic deformation of the foil and its supports are simulated by a finite-element model. The steady-state, quasi-transient and full transient dynamics of the foil-fluid-journal interaction are examined. For the steady-state simulation of a particular journal position, the fluid lubricant pressures are evaluated by means of a joint iterative scheme until convergence is achieved in both the fluid pressure and the corresponding foil deformation. For the quasi-transient case, the transient motion of the journal is calculated using a numerical integration scheme for the velocity and displacement of the journal. The deformation of the foil is calculated through numerical iteration in the feedback mode in combination with the fluid film pressure generated by the journal motion, until convergence at every time step is achieved. For the full transient simulation, a parallel real-time integration scheme is used, at each time step, to simultaneously evaluate the new journal position and the new deformed shape of the foil.     

Wear Behavior of Thin Film Heads for VCR in Sliding with Metal Evaporated Tapes

In order to apply thin film heads to digital video cassette recorders, wear behavior, machinability of head materials, and level difference of the heads were evaluated. The tests, performed with metal evaporated tapes, were divided into two stages. First, wear rate and machinability of individual materials were evaluated. It was found that adhesive wear was dominant for every material. Wear damage was especially-severe for metal magnetic films. Machinability was satisfactory for most bulk materials except for those with a hardness of more than 1000 kgf/mm², ZrO₂ ceramics and devitalized glass. Secondly, wear damage and level difference were evaluated using model heads. After the test, a number of flows were formed on sliding surfaces, mainly on the film surfaces, indicating that abrasive wear occurred. With bulk material of larger wear rate, the level difference reached the final value faster and its deviation was smaller. With Co-Zr-Nb magnetic metal and an Al₂O₃ protective layer, the level difference was less than 20 nm using CaTiO₃ or ZrO₂-Ta₂O₅, bulk substrates.     

Modification of Tribological Properties of Silicon by Boron Ion Implantation

Friction and wear properties of silicon used in the fabrication of microelectromechanical systems (MEMS) are important for their long-term reliability. In the present study, the authors have implanted single-crystal and polycrystalline silicon wafers with boron ions to improve their mechanical and tribological properties. The authors have studied the effects of ion implantation on the crystallinity, microstructure, nanohardness, and friction and wear properties and have found that silicon remains crystalline after ion bombardment at doses up to 2 × 10¹⁷ ions.cm^?2 but with a large amount of defects. The ion bombardment modifies elastic/plastic deformation characteristics and crack nucleation that occurs during indentation. There is a minor increase, ? 10-15 percent, in the nanohardness as a result of boron-ion implantation. Ion bombarded single-crystal silicon exhibits very low friction (0.05) and low wear factor (10^?6 mm³·N^?1m^?1) while slid against a 52100 steel ball. The coefficient of friction of bombarded silicon in dry air and dry nitrogen is even lower.     

轴颈质量对动载滑动轴承润滑状况影响的研究

本文采用动载滑动轴承轴心软迹的动力学计算方法,详细地讨论轴系惯性质量对动载滑动轴承轴心软迹和润滑状况的影响,以及转速对轴承润滑状况的影响。