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RESEARCH PAPERS

J. Tribol. 1989;111(2):193-199. doi:10.1115/1.3261886.

A new computational algorithm is developed for the numerical analysis of elastohydrodynamic (EHD) lubrication problems. This algorithm combines direct-iteration, Newton-Raphson, and multigrid methods into one working environment. Accurate solutions for a wide range of steady-state, line-contact problems are obtained with a relatively small number of numerical operations. The algorithm can be used to efficiently simulate transient processes in EHD lubrication. It can also be extended to solve point-contact problems with high computational and storage efficiency.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):200-206. doi:10.1115/1.3261887.

The dynamic behavior of a noncontacting rotary mechanical face seal is analyzed. A closed-form solution is presented for the response of a flexibly mounted rotor to forcing misalignments which normally exist due to manufacturing and assembly tolerances. The relative misalignment between the rotor and the stator, which is the most important seal parameter, has been found to be time dependent with a cyclically varying magnitude. The relative response is minimum when support stiffness and damping are minimum. The gyroscopic couple is shown to have a direct effect on the dynamic response. This effect is enhanced at high speeds, and depending on the ratio between the transverse and polar moments of inertia, it can either decrease or increase the dynamic response. Its effect is most beneficial to seal performance when the rotor is a “short disk.” A numerical example demonstrates that a flexibly-mounted rotor seal outperforms a flexibly mounted stator seal with regard to the total relative misalignment, the critical stator misalignment, and the critical speed.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):209-214. doi:10.1115/1.3261890.

The properties of magnetic bearings, particularly those based on repulsive forces due to eddy currents, are determined by a complex mixture of electrical and mechanical length and time scales. A perturbation solution for the magnetic field structure based on careful ordering of these parameters has permitted the effects of realistic gap geometries to be analyzed. The load capacity of eddy current journal bearings is found to be somewhat larger than previously predicted in an earlier paper which used magnetic fields based on constant gap size. The present results may be of interest to those concerned with calculating eddy currents in conventional attractive magnetic bearings.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):215-219. doi:10.1115/1.3261891.

This paper presents an analysis of the performance characteristics for a misaligned full journal bearing operating in turbulent regime. The modified Reynolds equation for turbulent flow is solved taking into consideration that the distribution of the effective viscosity is dependent on local shear stress. It is found that journal misalignment influences bearing behavior especially at lower eccentricity ratios. Also, it is concluded that for the same load carrying capacity misaligned journal bearing consumes more power than an aligned one.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):220-227. doi:10.1115/1.3261892.

General analyses are developed to predict the role of surface roughness, rarefaction effects, and various operating parameters in thin-film gas lubrication. Both shear- and squeeze-film effects are considered. The squeeze-film analysis is developed for transient and periodic motions. The analyses are based on average flow (roughness) factors. The results are presented in terms of Knudsen number, h/σ (film thickness/standard deviations of composite roughness) and roughness-orientation parameters. The appropriate analyses presented in this paper are simple and can be applied to magnetic recording and other applications to provide design guidelines.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):228-237. doi:10.1115/1.3261893.

Surface roughness-induced hydrodynamic gas lubrication theory including rarefaction effects is used to explain the effects of surface roughness on the magnetic head-medium spacing. Since video-recording operates at h/σ (film thickness/standard deviations of composite roughness) ≤ 3, the spacing increases with the roughness because the head surface remains at the distance on the order of 3σ from the mean of the tape surface. Data processing tapes operate at h/σ ≥ 4, and the increase in spacing with the roughness is found to be due to roughness-induced squeeze films. Squeeze motion can be generated by the isolated high asperities on the tape surface and bearing load variations due to a moving roughness (in shear flow) which are expected to increase with an increase in the surface roughness, and modulations of surfaces from other instabilities. Increase in signal-to-noise ratio and in amplitude variation for a rougher tape is also explained by the surface roughness variations. Influence of surface roughness on the head-disk spacing is also analyzed. Recommendations are made for an optimum roughness orientation and magnitude and whether the roughness should lie on the stationary or moving surfaces.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):238-244. doi:10.1115/1.3261896.

A micro-computer supported, rule-based expert system for failure diagnosis of tribo-components is described. Included is a brief review of AI tools and system organization methods used. The system, as implemented, encompasses: (a) observation of the machine or device containing the tribo-components; (b) identification of component failure modes by visual appearance comparison with photographic standards, and (c) reverse-engineering of the component selection for the application. Not implemented, but defined are: laboratory and advanced analytic diagnostic methods. The system consists of interactive screen-dialogs, augmented by engineering computation routines and followed by the generation of formatted diagnostic and corrective action reports.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):246-251. doi:10.1115/1.3261900.

The film thickness and pressure in elastohydrodynamically lubricated conjunctions have been evaluated numerically for a rather complete range of operating parameters (dimensionless load, speed, and materials parameters) normally experienced in practical applications. From the film thickness and pressure throughout the conjunction a number of performance parameters were evaluated. By curve fitting the data, formulas were obtained that allow easy evaluation of the amplitude and location of the pressure spike, the minimum and central film thicknesses, the value of ρ e He , and the center of pressure.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):252-259. doi:10.1115/1.3261901.

The state variable filter method of parametric identification is applied in the determination of squeeze-film dynamic coefficients from forced excitation tests on an experimental rig. The experimental squeeze-film damper had a centralizing spring, a central circumferential oil feed groove, and no end seals. Forced excitation tests are recorded at various journal support system natural frequencies and at different journal eccentricities. From these tests, estimates of the direct squeeze-film damping, stiffness and inertial coefficients are derived and presented. These results are shown to be in good agreement with results recently obtained using an independent frequency domain technique. The experimental damping and inertial coefficients were found to be considerably larger than values predicted by conventional short-bearing theory, but relatively insensitive to the support system’s natural frequency (and the forcing frequency) for most of the range investigated. The fluid film stiffness coefficient values at low values of the system’s natural frequency agreed with results from static stiffness tests. Two geometrically identical journals were used, one of steel and one of a low-weight, magnesium alloy. The use of the low weight journal markedly reduced the scatter in the inertial and film stiffness coefficients.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):260-264. doi:10.1115/1.3261902.

Most previous studies of boundary lubrication have ignored the contribution of surface roughness to friction. However, recent work by Moalic et al. (1987) has shown that when asperity contacts can be modelled by a slip line field, there is a precise relation between the friction coefficient and the asperity slope. Here, it is shown that there is also a relation between the friction coefficient and the normal pressure for rough surfaces which can be predicted from a development of the slip line field model.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):265-269. doi:10.1115/1.3261903.

The analysis of actual lubrication problems needs to take into account particularities in the flow coming from kinematic conditions and contact geometry. For hybrid journal bearings lubricated by low dynamic viscosity fluid, turbulence and pressure drops due to inertia forces in the recess outlets are phenomena which must be taken into account to compute their working characteristics. A global method of study of lubricated contacts in isothermal laminar or not laminar flow by finite element method is presented. It can solve a great number of lubrication problems. A new type of approximation element for lubrication (Hermitian type) is used because it offers the following advantages: The nonlinearities in lubrication which come from turbulence phenomena, geometrical discontinuities (pressure drops) or boundary conditions (recess pressure) require the derivation of unknown functions. Added interpolations are not necessary to determine these values because the nodal unknowns are the values of the function and its derivatives in the two directions. As the modified Reynolds equation is in Cartesian coordinates, in the case of closed geometries such as journal bearings, joining is done just by nodal identification which guarantees continuity of the pressure and of its derivatives. The validity of this numerical model is realized with an experimental study done with a three recess hybrid journal bearing for different kinematic and geometric configurations. In a general way, experimental and theoretical results are in good agreement.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):270-276. doi:10.1115/1.3261904.

This paper deals with the problem of an asperity-excited thermo-mechanical field in a medium with a thin surface layer and a near surface void defect. The solutions for the temperature distribution and stress state in the vicinity of the void are obtained. Numerical results are obtained using the material properties of Stellite III for both the coating and the substrate. The parametric effects of material properties in the coating and the substrate are considered by varying the corresponding property in the coating or the substrate. The stress field solutions of the coated medium with a cavity are compared with the solutions for a single material with a cavity. In the case of the single material with a cavity, while the thermal stress is much larger than the thermal stress of the no cavity case, the principal directions of the thermal stress are not significantly changed. However, for the case of a coated medium with a cavity, not only is the thermal stress much larger than that of the no cavity case, but also the principal directions of the thermal stress are changed. The principal directions of the thermal stress field depend on both the material properties and the ligament thickness (thickness between the wear surface and the top edge of the cavity). When the angle of the principal directions becomes larger, shear delamination will initiate at the coating/substrate interface.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):278-287. doi:10.1115/1.3261907.

The general motion of a roller and the cage in a tapered roller bearing is modeled as a function of frictional behavior in the bearing and cage clearances. Roller skew is shown to increase with increasing friction. At relatively high friction and low cage pocket and guide land clearances, the roller tends to pivot in the cage pocket such that it is in steady contact on one side of the pocket while the contact is cyclic on the other side with the roller skew frequency equal to its angular velocity. Such a pivoting motion promotes a high-frequency whirl of the cage which is clearly seen both in the whirl orbit and the whirl velocity solutions. As the friction in the bearing reduces such a high-frequency whirl is completely eliminated. When the cage clearances are somewhat larger, nominal cage whirl, with an almost circular orbit and with whirl velocity equal to cage angular velocity, is produced at higher values of friction. Again the whirl gradually subsides as the friction in the bearing is reduced. The results demonstrate significance of the computer modeling approach to optimizing bearing design under prescribed frictional behavior and operating environment.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):288-292. doi:10.1115/1.3261908.

The paper presents a simple theory for predicting seizure times for journal bearings. Under conditions of insufficient lubrication when bearing friction is high, seizure is predicted to occur in less than 20 seconds of operation. Insufficient lubrication can occur during bearing start-up, application of unusual loads, or as a result of an interruption of the lubricant supply system. Three examples where bearing seizure has been observed are discussed and the actual times to seize are compared with theoretical predictions. The actual seizure times are slightly less than predicted by theory, which is probably the result of bearing imperfections or uneven loading not considered in the theory.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):293-300. doi:10.1115/1.3261911.

Test results are presented for leakage and rotordynamic coefficients for seven honeycomb seals. All seals have the same radius, length, and clearance; however, the cell depths and diameters are varied. Rotordynamic data, which are presented, consist of the direct and cross-coupled stiffness coefficients and the direct damping coefficients. The rotordynamic-coefficient data show a considerable sensitivity to changes in cell dimensions; however, no clear trends are identifiable. Comparisons of test data for the honeycomb seals with labyrinth and smooth annular seals shows the honeycomb seal had the best sealing (minimum leakage) performance, followed in order by the labyrinth and smooth seals. For prerotated fluids entering the seal, in the direction of shaft rotation, the honeycomb seal has the best rotordynamic stability followed in order by the labyrinth and smooth. For no prerotation, or fluid prerotation against shaft rotation, the labyrinth seal has the best rotordynamic stability followed in order by the smooth and honeycomb seals.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):302-308. doi:10.1115/1.3261914.

Numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed, utilizing a multigrid iterative technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):309-314. doi:10.1115/1.3261915.

In the past, the mechanics of repeated rolling and sliding contact could only be treated for the idealized, elastic-perfectly-plastic (and isotropic) cyclic materials behavior, albeit approximately. They have not proven useful because the real cyclic plastic behavior of contacting materials is anything but perfectly plastic or isotropic. Using finite element methods, the authors have developed techniques for treating elastic-linear-kinematic hardening-plastic (ELKP) behavior, an idealization that comes much closer to the behavior of low, medium, and high hardness steels. In an earlier paper, the authors have examined rolling and sliding on rail steel, which is much softer than hardened bearing steel and displays quite different ELKP properties. The present paper offers the first results for repeated rolling and sliding for high strength bearing steel ELKP behavior and material properties.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):315-322. doi:10.1115/1.3261916.

The friction-induced thermal energy at the contacting surface increases the contact temperature which changes the material properties and produces thermal stresses in the body. Plastic yielding of the contacting bodies resulting from the combined thermal and isothermal effects is investigated. An associated wear mechanism controlled by plastic deformation is introduced, and a wear control approach is presented.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):323-330. doi:10.1115/1.3261917.

This paper describes a theoretical analysis that can be used to study every periodic roughness pattern effects when Reynolds equation is valid. Numerical results using this new “averaged” equation point out the field of application of the method, particularly with respect to the roughness wavelength.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):331-336. doi:10.1115/1.3261918.

Magnetic bearings are subject to performance limits which are quite different from those of conventional bearings. These are due in part to the inherent nonlinearity of the device and in part to its electrical nature. Three important nonideal behaviors are presented: peak force capacity, force slew rate limitation, and sensitivity to rotor motion at large displacements. The problem of identifying the dynamic requirements of a magnetic bearing when used to support a known structure subject to known loads is discussed in the context of these limits. Several simple design tools result from this investigation.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):337-343. doi:10.1115/1.3261919.

A friction factor model is developed for the entrance-region of a duct. The model is used in an annular gas seal analysis similar to Nelson’s (1984). Predictions of the analysis are compared to experimental results for a smooth-stator/smooth-rotor seal and three honeycomb-stator/smooth-rotor seals. The model predicts leakage and direct damping well. The model overpredicts the dependence of cross-coupled stiffness on fluid prerotation. The model predicts direct stiffness poorly.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):344-351. doi:10.1115/1.3261920.

The effects of lubricant rheology and surface kinematic conditions on micro-elastohydrodynamic (EHD) lubrication are analyzed under isothermal line-contact conditions. Micro-EHD lubrication is modeled by introducing a surface irregularity in the form of an asperity or a furrow into the contact zone. Under simple sliding conditions, the pressure generated in the vicinity of the irregularity and the resulting surface deformation depend strongly on the lubricant rheology. The surface kinematic conditions have profound effects on micro-EHD lubrication. In general, a stationary surface irregularity produces a relatively strong downstream effect when it is in the inlet region of the contact, and a moving surface irregularity produces a relatively strong upstream effect after it enters the Hertzian central region. The simulated results agree qualitatively with previous experimental measurements and observations.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):352-357. doi:10.1115/1.3261921.

To reduce the frictional power loss of hydrostatic thrust bearings, the hydrostatic thrust bearing with a floating disk shaped in a simplified configuration is proposed. And the load capacity and the frictional torque are experimentally investigated in laminar and superlaminar regimes. Following results can be obtained: (1) The disk floats at a certain stable position for given shaft rotational speed and rotates at nearly half rotational speed of the shaft. (2) The frictional torque of this type of the bearing is less than half of a conventional hydrostatic thrust bearing with the same surface configuration as the floating disk.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):359-363. doi:10.1115/1.3261924.

A brief summary of the methods commonly used for the analysis of rough surfaces and the errors associated with these techniques is given. A frequency domain digital differentiator is shown to reduce the bias errors for estimates of the properties of slopes and curvatures for a sample spacing determined by the profilometer probe size. A comparison of this “spectral” approach with finite difference methods for calculating slope and curvature characteristics for a ground surface show substantial underestimates for the latter methods.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):364-371. doi:10.1115/1.3261925.

The load on the larger tilting pad bearing can be as high as 106 N. With such high static loads, pad and pivot distortions and thermal effects in the lubricant cannot be neglected. This paper analyzes the influence of the deformation of the pads and pivots on the static and dynamic behavior of typical turbo-generator tilting pad bearings used in actual operating conditions. Thermal and pressure distortions are compared. The hydrodynamic pressures and lubricant temperatures are computed with a three-dimensional model. Thermal and elastic pad and pivot distortions are obtained with a three-dimensional finite element model.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):372-377. doi:10.1115/1.3261926.

The laser beam treatment of magnesia partially stabilized zirconia (Mg-PSZ) sample surfaces has shown a considerable improvement in their wear resistance and surface hardness. The laser beam treated surfaces exhibited higher wear resistance than either ground untreated or ground and laser treated ceramic surfaces. There are optimum combination of the laser treatment process parameters (laser power and exposure characteristics) that resulted in the minimum wear rate or the maximum surface hardness. There was no correlation found between the wear rate and the surface hardness. There were two wear mechanisms operational, namely, surface fracture and surface polishing. The treatment of the ceramic surfaces reduced the fracture component of the wear rate. The laser treatment effect on the polishing process was not detected. The increase in the wear resistance and the surface hardness of the laser beam treated surfaces were due to the thermally induced phase transformations resulted in the formation of the compressive stress field on the surface and altering the surface structure.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):378-384. doi:10.1115/1.3261927.

The static and dynamic characteristics of annular plain seals were investigated theoretically in the turbulent flow regime. The turbulence model which uses the nonlinear analysis developed by Elrod and Ng has been improved for Reynolds numbers higher than 100,000 to include cryogenic application. In addition, velocity boundary conditions have been reexamined. The two-dimensional Reynolds equation was solved numerically considering the swirl effect and the pressure drop due to axial acceleration of liquid at the inlet of the seal. Integration of the pressure distribution defines the reaction force developed by the seal and the corresponding rotordynamic coefficients. The solution applies for taper geometry of eccentric seal and variable fluid properties.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

TECHNICAL BRIEFS

J. Tribol. 1989;111(2):386-390. doi:10.1115/1.3261930.

This paper deals with the development of a dimensionless empirical formula for calculating the coefficient of friction in sliding-rolling steel on steel contacts under different operating conditions in the thermal regime. The effect of lubrication, surface roughness, and surface coating on friction are considered. The formula shows excellent correlation with the experimental tests conducted by many investigators and provides a unified relationship for all the published data.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(2):390-393. doi:10.1115/1.3261931.

This technical note presents an approximate solution for the fluid film forces and design coefficents for statically loaded cylindrical journal bearings. The solution is an improved correction to the infinitely long journal bearing model. The formulas derived are of extreme simplicity and the results are excellent for most practical journal bearing configurations.

Commentary by Dr. Valentin Fuster

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