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RESEARCH PAPERS

J. Tribol. 1992;114(3):403-411. doi:10.1115/1.2920899.

Friction and wear experiments were conducted on high purity alpha-alumina sliding against a similar material in air under different contact loads and at temperatures ranging from 23°C to 900°C. Experimental results indicate that tribochemical reactions between water vapor and alpha-alumina at room temperature produce aluminum hydroxide which results in relatively low coefficients of friction and low wear rates. Both the coefficient of friction and the wear rate of alumina were low at intermediate temperatures (200°C to 800°C), if the contact stress was below a threshold value. Above this load, wear occurred by fracture, the wear coefficient exceeded a value of 10−4 , and the coefficient of friction increased to 0.90. At 900°C, the coefficient of friction was 0.40 and the wear coefficient was reduced to a value less than 10−6 , because of the formation of a silicon-rich layer on the wear track. A contact mechanics model based on linear elastic fracture mechanics indicated that propagation of cracks from pre-existing flaws controls the onset of catastrophic wear in the intermediate temperature range.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):412-419. doi:10.1115/1.2920900.

The paper describes the results of an elastohydrodynamic lubrication (EHL) analysis of an elliptical contact between a rough, stationary surface and a smooth, moving surface. The roughness consists of two-dimensional grooves/ridges aligned in a direction perpendicular to that of lubricant entrainment, and is sinusoidal in profile with two scales of wavelength and amplitude. The main feature of these results is the significant degree of asperity deformation and corresponding ripple in the pressure distribution. Also presented are preliminary results of a line contact EHL analysis in which profiles from real surfaces are used to simulate the lubrication of gear teeth at high temperatures. These results show significantly less proportional reduction of roughness due to asperity deformation.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):420-430. doi:10.1115/1.2920901.

A thermal analysis has been used to predict transient temperature rises at a typical head-particulate-disk interface and a head-thin-film-disk interface. Thermal properties of the various thin-films used in the construction of magnetic rigid disks are measured. Average and maximum transient temperature rises for the assumed head-particulate-disk interface over the contact area are 34 and 44°C, respectively for an Al2 O3 -TiC slider. If the exposed magnetic particles or alumina particles contact the slider surface, the transient temperature rise could be more than 1000°C. Average and maximum transient temperature rises for the assumed head-thin-film-disk interface over the contact area are 56 and 81°C, respectively for an Al2 O3 -TiC slider and 77 and 110°C, respectively for an Mn-Zn ferrite slider. The durations of asperity contact generally are less than 100 ns. The thermal gradients perpendicular to the sliding surfaces are very large (a temperature drop of 90 percent in a depth of typically less than a contact diameter or less than a micron).

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):431-438. doi:10.1115/1.2920902.

An analysis is developed to calculate the static and dynamic characteristics of annular eccentric seals. Effects of inertia forces in the film, tapered geometry and rotor misalignment are taken into account. Derivation of the governing equations for incompressible flow is based on the Navier-Stokes equations, the continuity equation and a turbulence model using the nonlinear analysis developed by Elrod and Ng. The inlet boundary conditions define the initial swirl and the pressure drop due to the fluid acceleration. Perturbation of the flow variables yields a set of zeroth-order and first-order equations. Integration of the zeroth-order equations yields the steady-state solution which defines the seal leakage, the static load and the moment of misalignment. The eccentric and misaligned rotordynamic coefficients are obtained by integration of the first-order pressure equations. Comparisons are made between the stiffness, damping and inertia coefficients derived herein and both theoretical results based on other models and experimental data which were previously published.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):439-447. doi:10.1115/1.2920903.

An elastic-plastic impact model for spheres is introduced as the basis to study the normal impact of rough surfaces. Statistics is applied to arrive at the ensemble behavior of many unit events alluded above, allowing the investigation of surface roughness effects. Dissipation of kinetic energy increases such as surface roughness, material compliance, and impact velocity is increased. The rebound velocity is shown to be dependent on surface topography and material properties, in addition to impact velocity.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):448-454. doi:10.1115/1.2920904.

The traditional approach is to characterize the behavior and performance of fluid film hydrodynamic journal bearings by means of linearized bearing analysis. The objective of this paper is to examine the nonlinear characteristics of the said journal bearing. Results based on bearing stiffness characteristics, steady and transient vibration orbits, and frequency response functions obtained from both linear and nonlinear bearing simulations are compared with each other. Conclusions are drawn from the results obtained from a prototypical bearing configuration used as an example in this analysis.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):455-461. doi:10.1115/1.2920905.

This paper analyzes the effects of multiple cracks situated in the contact zone vicinity of an elastic isotropic component, modeled as a half-plane. Friction between the crack faces is taken into account using Coulomb’s law. Straight arbitrarily oriented cracks are considered. Any contact condition can be modeled between the crack faces as well as any loading condition over the half-plane surface, including complete loading cycles. The method has been tested for up to 5 cracks and shows no limitation in crack number. Further, the method is general as no prior assumptions concerning the state of the crack, i.e., the slip-stick-open configurations along the crack are required. The stress intensity factors (SIFs) calculated for two crack configuration are compared with those obtained for single cracks.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):462-468. doi:10.1115/1.2920906.

A semianalytical model of multiple fatigue crack analysis in sliding contact is developed. Linear elastic fracture mechanics is applied. Frictional resistance between crack faces is taken into account. Five crack interaction mechanisms have been identified. Load transfer between cracks can cause both significant increases and drops in stress intensity factors both in mode I and II. The interaction depends on the distance between cracks, their relative position with respect to the loading zone, and the interfacial crack coefficient of friction.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):469-476. doi:10.1115/1.2920907.

Basic flow relationships are developed for three typical non-Newtonian lubricant models: the pseudo-plastic model, the circular viscoplastic model, and the ideal viscoplastic model. It is found that the conventional no-slip boundary conditions are inadequate to fully treat the latter two models. Conclusions regarding the appropriate boundary conditions for any viscoplastic model and the form of the resulting Reynolds equations are presented.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):477-484. doi:10.1115/1.2920908.

The Reynolds equations for viscoplastic lubricants can be quite complex, involving multiple branches which depend on the form of the boundary conditions invoked in their development. Methods of visualizing and understanding the branching problem are explored. This information is used, together with the Reynolds equations developed in the companion paper, in analyses of the lubrication of a wide slider bearing and a metalforming inlet zone. The results of these analyses are used to draw general conclusions regarding the influence of different types of non-Newtonian behavior.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):485-491. doi:10.1115/1.2920909.

The flow field within the lubricating film of a rotating shaft lip seal containing microundulations is analyzed numerically. The results demonstrate that the action of the microundulations can prevent leakage through the seal. The effects on leakage rate of shaft speed, undulation amplitude and wavelength, shear deformation of the undulations, flattening of the undulations, and axial lip profile are presented.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):493-498. doi:10.1115/1.2920910.

Scanning Tunneling Microscopy is used to modify and measure the surface of magnetic media disks. A very rugged diamond tip allows continued scanning after it has severely scratched or punched the surface. Three techniques are used. First a manual method of penetrating the surface using a stand-alone head makes a scratch of essentially uncontrollable length and depth. Then the normal head is used to cause surface penetration by removing the bias voltage while scanning. Better control is obtained as regards the location and depth of the indentation. Excellent control of indentation location and depth can be obtained by using a new software developed by the STM manufacturer to push the tip into the surface with the piezoelectric scanner. The control of the indentations and their subsequent measurement may make the STM a useful tool as a hardness tester for ultra-thin films, on the order of a few tens of nanometers.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):499-503. doi:10.1115/1.2920911.

In this paper the optimum geometrical configurations of a shrouded Rayleigh-step and a spiral groove viscous pump are analyzed. Then their performance characteristics are compared. The geometries and film shapes of these viscous pumps are optimized with respect to flow rate and the design parameters are summarized graphically. The flow rate of the optimized spiral groove viscous pump is approximately 5–10 percent greater than that of the optimized shrouded Rayleigh-step viscous pump.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):507-514. doi:10.1115/1.2920912.

The parameters that appear to determine if slider-disk contact occurs during dynamic loading are the relative loading velocity at the instant of load and the initial pitch and roll of the slider at its unloaded state. A dual-beam LDV system is employed in this study to measure the displacement, pitch, and roll during dynamic loading for five different standard 3380-type sliders in order to investigate the effects of the initial pitch and roll. The effects of the initial height and control loading speed are also examined by using the dual-beam LDV and acoustic emission (AE). Based on the experimental results, we propose several slider-disk contact criteria. Among them, the criterion based on the initial diagonal slope and the peak loading velocity gives a simple way to predict if slider-disk contacts will occur, but it overlooks the effect of the signs of the initial pitch and roll. A three-dimensional criterion based on the peak velocity and the initial pitch and roll angles appears to be more reliable. Using either criterion, it is found that high peak loading velocity causes slider-disk contact, and sliders with larger initial pitch or roll angles are more likely to hit the disk.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):515-521. doi:10.1115/1.2920913.

A viscous pump design that is capable of producing higher flow rates than a viscous pump previously introduced by Etsion and Yaier (1988) is developed and investigated. The key to the new design is straight lobes as opposed to the semicircular lobes of the previous design. The geometry of the straight lobes does not lend itself to as straightforward a solution as the semicircular lobe analysis. Approximations are made and then verified using upper and lower shape factor bounds and finite element analyses. Lobe geometry for each lobe design is optimized to produce maximum pumping capacity. The results of the optimization show that the straight lobe pump is theoretically superior to the semicircular lobe pump.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):524-529. doi:10.1115/1.2920914.

This paper describes a new type of wear test rig which is based on a quick stop principle. The advantages of using such a rig and the associated testing method are described with respect to the analysis of prow formation.

Topics: Wear , Testing , Wear testing
Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):530-538. doi:10.1115/1.2920915.

Factors contributing to the dynamic instability of ball retainers in precision bearings were investigated. A real-time, rolling-element bearing dynamics simulation was written (PADRE - Planar Analysis of a Dynamic Retainer) for rapid evaluation of key bearing design factors. This code permits economic screening of a large number of bearing geometric parameters as a prelude to other more comprehensive dynamic bearing codes. The simulation uses a recently-developed integration package to increase computational speed and accuracy, and also employs a simplified lubricant traction model due to Johnson and Tevaarwerk. Tests with precision angular-contact ball bearings verified important features of this analysis including friction threshold for instability, retainer motion, and the instability frequency. Retainer instability was found to be highly sensitive to retainer-ball friction and exhibited a constant characteristic frequency, which was independent of speed, external vibration, radial load, and preload.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):540-551. doi:10.1115/1.2920916.

A complete solution is obtained for elastohydrodynamically lubricated conjunctions in line contacts considering the effects of temperature and the non-Newtonian characteristics of lubricants with limiting shear strength. The complete fast approach is used to solve the thermal Reynolds equation by using the complete circular non-Newtonian fluid model and considering both velocity and stress boundary conditions. The reason and the occasion to incorporate stress boundary conditions for the circular model are discussed. A conservative form of the energy equation is developed by using the finite control volume approach. Analytical solutions for solid surface temperatures that consider two-dimensional heat flow within the solids are used. A straightforward finite difference method, successive over-relaxation by lines, is employed to solve the energy equation. Results of thermal effects on film shape, pressure profile, streamlines, and friction coefficient are presented.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):553-562. doi:10.1115/1.2920917.

This paper presents a mathematical model for piston skirts in mixed lubrication. It takes into account the effects of surface waviness, roughness, piston skirt surface profile, bulk elastic deformation and thermal distortion of both piston skirts and cylinder bore on piston motion, lubrication and friction. The corresponding computer program developed can be used to calculate the entire piston trajectory and the hydrodynamic and contact friction forces as functions of crack angle under engine running conditions. This paper is the first part of a series of two papers. It gives basic information and some preliminary results. The second part will include the major results and discussions, focused on the influences of elastic and thermal deformations.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):563-566. doi:10.1115/1.2920918.

The existing narrow-groove theory is used for evaluating leakage flow for various configurations which might be of interest in seal design, including variable angle, film thickness and groove/ridge length ratio.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):567-578. doi:10.1115/1.2920919.

The planar dynamics of a rough block in nominally stationary or sliding contact with a counter-surface is studied in this work. Starting with the Greenwood-Williamson model of a rough surface, the analysis of elastic contact deflections is extended to accommodate angular as well as normal motions. The real area of contact and the normal contact force are obtained in terms of the relative approach and orientation of the surfaces. It is shown that angular and normal motions at frictional contacts are generally coupled. The contact area and normal contact force are shown to be nonlinearly related to the normal and angular motions. However, the contact area remains proportional to the normal load, even in the presence of angular motions. When the friction force is assumed to be proportional to the real area of contact, the coefficient of sliding friction will be unchanged by small relative rotations between the sliding bodies. Based on this contact and friction model, the nonlinear equations of motion that describe the planar contact vibrations of a sliding block can be written directly. Although a detailed analysis of the stability and response characteristics of these nonlinear equations is beyond the scope of the present work, a limited comparison of calculations and measurements taken on both stationary and sliding blocks indicate that the small amplitude contact vibrations are reasonably well captured by the model developed in this work.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):579-587. doi:10.1115/1.2920920.

Operating characteristics of four-shoe tilting-pad journal bearings of 100 mm diameter and 70 mm length are determined on an experimental device. The load, between pad configuration, varies from 0 to 10,000 N and the rotational speed is up to 4000 rpm. Forty thermocouples are used in order to measure bearing element temperatures (babbitt, shaft, housing and oil baths). The influence of operating conditions and preload ratio on bearing performances are studied. Comparison between theoretical and experimental results is presented. The theoretical model is also performed on a large tilting-pad journal bearing which was investigated experimentally by other authors.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):589-594. doi:10.1115/1.2920921.

The frictional resistance generated by a ball bearing, when starting from rest, increases to a free rolling value in a finite amount of time instead of experiencing an instantaneous step increase. This is due to the complex ball dynamics involved. A change in the direction of rotation results in a reversal of the bearings dynamic torque characteristics. When a traversing process is continuously repeated, the friction torque of the bearing traces out hysteresis loops. This phenomenon is often described as ball jitter. An apparatus was built to study the ultra-low-speed hysteresis behavior found in jittering ball bearings. This behavior was first modeled by P. R. Dahl (1968). He found torque hysteresis loops to be characterized by the steady rolling friction torque, Ts , and the reversal torque slope, σ. A theoretical expression for Ts has been verified in previous research by Lovell et al. (1991), but no expression for σ has currently been determined at low speeds. Therefore, the experimental testing apparatus was canonically designed to incorporate three balls, rather than a full bearing. This was done in order that the characteristics of σ could be more readily determined, as many additional friction elements which occur in full bearings were eliminated. The effects of normal load, rotational rate, and lubrication regime on σ were all investigated using the testing apparatus. The experimental values obtained for the rest slope were coupled with previously determined values of Ts , so that empirical Dahl hysteresis curves could be generated. Excellent correlation was found to exist between the experimental jitter torque data and Dahl predicted dynamic torque behavior.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):595-599. doi:10.1115/1.2920922.

An analysis of roughness effects on leakage of lip seals is presented. The generation of fine axially oriented striations has been seen to occur on some lip seals after a certain time of operation, Müller and Ott (1984). Kammüller (1986) and Müller (1987) have suggested that under running conditions, the striations may be distorted due to differential shear stresses leading to a channelling or pumping action of the grooves. This may balance the flow due to the pressure difference over the seal and thus suppress leakage. The roughness theory of the first author has been combined with the roughness pattern distortion theory of the second author. The resulting model is seen to predict a complete leakage suppression under realistic conditions.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):600-605. doi:10.1115/1.2920923.

The perturbation method, aided by symbolic computation software, is employed to solve Maxwell’s equations to obtain theoretical predictions of forces and stiffness and damping coefficients for a simplified eddy current magnetic bearing. The results show that this kind of bearing has low stiffness and extremely low damping compared to conventional bearings. In fact, the damping is probably negative in most cases. In addition, the cross-coupled stiffness is relatively high, further contributing to rotor-dynamic problems. Despite these drawbacks, if advanced high temperature superconducting materials become practical, eddy current magnetic bearings may be useful in many applications.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):606-611. doi:10.1115/1.2920924.

This paper gives closed-form expressions in terms of elementary functions for the title problem of spherical Hertzian contact of elastic bodies possessing transverse isotropy. Traction in the contact region is also included in the form of Coulomb friction; thus the shear stress is proportional to the contact pressure. The present expressions derived here by integration of the point force Green’s functions are simpler and easier to apply than equivalent expressions which have previously been given.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):612-615. doi:10.1115/1.2920925.

Two formulas, one for the characteristic time of filling a void with the vapor of the surrounding liquid, and one of filling the void by diffusion of the dissolved gas in the liquid, are derived. By comparing these time scales with that of the dynamic operation of oil film bearings, it is concluded that the evaporation process is usually fast enough to fill the cavitation bubble with oil vapor; whereas the diffusion process is much too slow for the dissolved air to liberate itself and enter the cavitation bubble. These results imply that the formation of a two phase fluid in dynamically loaded bearings, as often reported in the literature, is caused by air entrainment. They further indicate a way to simplify the treatment of the dynamic problem of bubble evolution.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):616-622. doi:10.1115/1.2920926.

In this paper the influence of surface roughness on the pressure profile and film thickness in a steady state EHL line contact is investigated using input from an actually measured roughness profile in the calculations. Pressure profiles and film shapes for different load conditions are shown. The presented results strongly indicate that in the steady state situation considered here a significant deformation of the roughness profile occurs. As a result the often used λ parameter being the ratio of film thickness and standard deviation of the roughness (h/σ) with σ based on the undeformed roughness profile may give misleading information as far as the effect of the roughness on pressure and film shape is concerned.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):623-629. doi:10.1115/1.2920927.

A method of solution for laminar channel flow is established using the von Mises transformation followed by the “separation” of the main flow velocity into amplitude and profile functions. The known boundary conditions on the latter enable a generalized solution that yields, through a parametric relation between auxiliary parameters (the characteristics), a system of ordinary differential equations for the velocity amplitude and the pressure. The result is a powerful semi-analytical method which is very easy to implement for a variety of internal flow configurations. The method is, in essence, a downstream general solution which may be extended upstream to the singular limit of a uniform main flow velocity distribution at the channel entrance. The regular solution for uniform initial velocity distribution cannot thus be obtained. Comparisons with other solutions show only qualitative agreement, for reasons which are discussed, whereas agreement with experimental results, made in a separate publication, is remarkably good.

Commentary by Dr. Valentin Fuster
J. Tribol. 1992;114(3):630-636. doi:10.1115/1.2920928.

After a short survey of the different methods and formulas used to determine the pressure distribution in radial (converging or diverging) flow between nominally parallel discs, the method of “separation of variables,” established in reference [1], is applied to the problem, especially the case pertaining to centrally fed circular aerostatic bearings. The results are compared extensively with experimental data from various sources and the agreement is found to be remarkably good, suggesting that a laminar flow model is sufficient in characterizing the flow over a wide range of Reynolds number values.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

BOOK REVIEWS

J. Tribol. 1992;114(3):637. doi:10.1115/1.2920929.
FREE TO VIEW
Abstract
Topics: Friction , Machinery
Commentary by Dr. Valentin Fuster

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