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RESEARCH PAPERS

J. Tribol. 1991;113(4):659-666. doi:10.1115/1.2920676.

An improved theoretical model for the hydrodynamic lubrication of axisymmetric, sheet metal stretch forming is presented. The infinite initial film thickness problem, encountered in a previous model, is removed by accounting for the squeeze action occurring during the initial stages of the process. Both isoviscous and thermoviscous theories are developed assuming that the lubricant is a Newtonian fluid. In the thermoviscous model, the lubricant viscosity is assumed to vary exponentially with temperature. The influence of plastic heating of the sheet on the entrainment and transport of the lubricant film is examined. The effects of variable punch speed are also investigated.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):667-674. doi:10.1115/1.2920677.

In order to test the validity of the theoretical model discussed in Part 1, an experimental technique, employing optical interferometry, has been developed to measure lubricant film thickness during axisymmetric stretch forming. Specially fabricated, transparent punches are used for both double and multiple beam interference studies. The choice of workpiece material, lubricant, and forming speed ensures that the punch/sheet conjunction will be hydrodynamically lubricated during most of the process. Interference patterns, due to the variable film of lubricant separating the punch and sheet surfaces, are formed as the sheet wraps around the punch. These patterns provide a contour map of the lubricant film thickness along the punch/sheet conjunction. The measured film thickness, as taken from an interpretation of the patterns, is compared with the theoretical predictions of Part 1.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):675-680. doi:10.1115/1.2920678.

This study involves the development of correlating equations for the prediction of the bulk moduli of mineral oil-based lubricants, polymer containing lubricants, and several classes of synthetic fluids including methyl silicones, perfluoropolyether, polybutenes, poly α-olefin, polyphenyl ethers, and esters. This technique only requires the viscosity, the density, and deviation factor which is related to structural effects and free volumes of the fluids. Although prediction techniques are available in the literature for mineral oils, this is the first study to consider the predictions of the bulk moduli of polymer solutions and nonmineral oil based fluids.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):681-688. doi:10.1115/1.2920679.

Mathematical relationships obtained on the basis of the friction theory in a wedge pair are widely used in technical calculations. With the help of them the limit circumferential force in cone clutches and friction drives with wedge-type bodies (wedge roller transmissions, variable-speed friction block belt drives, V-belt transmissions and etc.) are determined. This may seem to be a simple problem which could be solved without difficulties, however the classical equations used can not be derived in stringent terms and was not confirmed experimentally. The aim of this paper is to clarify this problem.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):689-693. doi:10.1115/1.2920680.

Friction tests on thin film magnetic disks with carbon overcoats were performed using commercial read/write heads as sliders. The results provide evidence that the thin film overcoats wear through chemical means in the presence of gaseous oxygen, and through mechanical means in the absence of oxygen. When small concentrations of water are present, friction behavior resembling that of an oxidizing environment is observed, suggesting oxidation of the carbon film preceded by dissociation of adsorbed water.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):694-702. doi:10.1115/1.2920681.

A computational analysis for calculation of the dynamic force response in turbulent flow annular pressure seals of arbitrary nonuniform clearance is presented. Cryogenic liquids are considered as barotropic. The fluid motion is described by a bulk flow model and Moody’s friction factor is introduced to accomodate surface roughness effects. The numerical solution scheme is computationally efficient and accurate for seal operation at arbitrary eccentricity ratios. Numerical predictions show good agreement with available experimental results. The effects of eccentricity and liquid properties on the performance of the Space Shuttle Main Engine High Pressure Fuel Turbopump interstage seal at full power level are discussed as a reference case.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):703-711. doi:10.1115/1.2920682.

A numerical solution to the problem of isothermal non-Newtonian elastohydrodynamic lubrication of rolling/sliding point contacts has been obtained. The multigrid technique is used to solve the simultaneous system of two-dimensional modified Reynolds and elasticity equations. The effects of various loads, speeds, and slide to roll ratios on the pressure distribution, film thickness, and friction force have been investigated. Results for the dimensionless load W = 4.6 × 10−6 and 1.1 × 10−6 , and the dimensionless velocity U = 3 × 10−10 and 3 × 10−11 are presented. The results indicate that slide to roll ratio has negligible effect on the minimum film thickness, however, it significantly reduces the pressure spike.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):712-718. doi:10.1115/1.2920683.

Surface pitting is a major failure mode for gears. Estimation of failure probability and service life are important in gear design. Current techniques give only a pass/fail rating based on semi-empirical methods. A predictive model for estimating service lives and failure probabilities has been developed. This paper discusses the life prediction analysis, which is based on propagation of a surface breaking crack under rolling/sliding contact conditions. The effects of both surface roughness and non-metallic inclusions can be included. While predicted lives are lower than expected, trends observed through parametric variation are consistent with service behavior.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):719-724. doi:10.1115/1.2920684.

A predictive pitting model for estimating failure probabilities and service lives has been developed. This paper presents the failure probability analysis and a discussion of the model’s application to spur gears. Probability estimates are based on an initial crack size distribution and on possible interaction between cracks and inclusions. Plots of the fraction of components experiencing pitting (percent) versus life show less spread than would be expected. However, trends predicted based on parametric variation are consistent with service behavior. The model is applied by linking the pitting model with a spur gear performance code. Results are compared with AGMA standards.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):725-728. doi:10.1115/1.2920685.

A new concept viscous pump that was described earlier in the literature was built and tested to evaluate its performance. It was found that the new concept is feasible and has promising features for use in various applications where high level of cleanliness is required. The pressure-flow characteristic is linear with an easy and accurate flow control which can be attractive in metering pumps.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):729-738. doi:10.1115/1.2920686.

The stress distributions associated with smooth surfaces in contact are rarely experienced in practice. Factors such as surface roughness, lubricant films, and third body particulates are known to influence the state of stress and the resulting rolling contact fatigue life. This paper describes a numerical technique for evaluating the complete subsurface field of stress resulting from the elastic contact of nonconforming rough bodies, based on measurements of their profile. The effect of sliding friction is included. The presence of asperities within the contact region gives rise to high shear stresses near the surface. Realistic coefficients of friction for lubricated sliding contacts (i.e., μ ≈ 0.1) causes the “smooth body” shear stresses to interact with the asperity stresses to produce a large, highly stressed region exposed to the surface. The significance of these near-surface stresses is discussed in relation to modes of surface distress which lead to eventual failure of the contacting surfaces.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):739-749. doi:10.1115/1.2920687.

The volumetric information storage density of rigid disk drives continues to increase through decreases in the slider-disk separation (i.e., the flying height). Reductions in slider-disk separations are achieved primarily through smoother surfaces on the magnetic media. The limiting factor in decreasing the slider-disk separation is the interactions that occur between the slider and the diminishing surface roughness and the impact that this roughness has on the transient and steady-state flying characteristics of the recording head. In this paper, we present a new finite element algorithm to solve the modified Reynolds equation that is specifically designed to utilize state of the art vector/parallel hardware. To the authors’ knowledge, this is the first numerical simulation of the flying characteristics of a finite width slider over a rigid disk surface which directly incorporates three-dimensional surface roughness. The effects that the magnitude, orientation, shape, and location (i.e., roughness on the disk or slider) of the surface roughness has on the steady-state slider flying characteristics are presented.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):750-754. doi:10.1115/1.2920688.

A theoretical model for an active squeeze film damper (SFD) is introduced. The design makes it possible to change the radial clearance and land length of the SFD by adjusting the position of the damper ring. Expressions for the oil film forces are obtained. The vibration control of a flexible rotor is taken as an example of the application of the new design. The possibility of controlling rotor vibrations is demonstrated by means of numerical experiments.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):755-761. doi:10.1115/1.2920689.

The surface roughnesses of two surfaces in a wear contact can change throughout the course of the wear process. This may or may not change the lubrication mechanism of the system depending on the real area of contact as influenced by the changes in the surface roughness. The present work examines the changes in surface roughness within the contact area, as well as the relative mating of the two surfaces. To quantify the similarity between the two wear surfaces, a new concept, the relative surface conformity, has been defined and developed. To effectively measure this parameter, a computer program was written to input the wear scar profilometry traces and to calculate the relative surface conformity of the two. Finally, the relative surface conformity was shown to rise with increasing test duration, during running in.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):762-767. doi:10.1115/1.2920690.

A theoretical approach is developed to determine capacitance, capacitive reactance, active resistance, and impedance of hydrodynamic journal bearings under different conditions of operation. It has been established that the bearing capacitance increases with eccentricity and L/D ratios but reduces with increase in clearance ratio. On the contrary, resistance and capacitive reactance of a bearing increase with the clearance ratio but reduce with increase in the eccentricity and L/D ratios. However, the bearing impedance is more affected by the resistance than the capacitive reactance. The bearing behaves like a capacitor till the ratio of capacitive reactance to active resistance is less than unity, and acts like a variable resistor as this ratio exceeds unity. This analysis has a potential to analysis safe load carrying capacity at different speeds of operation by determining the bearing capacitance. Also, this may act as a guide to select the bearing design parameters for safe and reliable operation of a hydrodynamic journal bearing.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):768-774. doi:10.1115/1.2920691.

This paper presents an overview of a finite-element-method (FEM) approach for the calculation of the dynamic stiffness of circular, externally pressurized gas thrust bearings with a nonuniform clearance. Some observations are made about the characteristic behavior of gas bearings subject to dynamic loading. The primary emphasis of this paper, however, is the development and qualification of a test apparatus and the necessary test techniques for measuring dynamic stiffness up to 250 N/μm at frequencies up to 2000 Hz. A thorough, experimental verification of the FEM model is reserved for a later paper.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):777-783. doi:10.1115/1.2920692.

In this paper a Multigrid extension of a stationary solver is outlined for the EHL solution of a line contact under transient conditions. The solver is applied to calculate pressure and film thickness profiles at each time step when an indentation is moving through the contact, which results in an asymmetric pressure profile. The time-dependent results are compared with the stationary solutions. The pressure as a function of time is presented as well as the integrated pressure (over time) as a function of the spatial coordinate. These time-dependent pressures are used to compute the sub-surface stress field, which shows higher stresses below the trailing edge of the indentation. Therefore the risk of fatigue is higher below the trailing edge of the indentation, as is experimentally observed. The transient pressures can be used for a fundamental study of the emitted frequency spectrum of rolling bearings, as used in condition monitoring.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):784-788. doi:10.1115/1.2920693.

Closed-loop stiffness and load capacity (force) equations have been developed for industrial magnetic bearings. Two sets of magnetic bearings have been constructed using these equations as a design basis. These bearings have been installed in two canned motor pumps. The predicted force and stiffness values from the equations are compared to experimental measurements to determine their validity. When obvious sources of error were eliminated, agreement within 10 percent was obtained for development pump’s magnetic bearings. Agreement was generally better for this pump than for the demonstration pump. By employing these equations, along with easily measured current and displacement information from magnetic bearing equipped machinery, actual stiffness’ and bearing loadings can be determined for operating equipment. Thus, the range of information available from magnetic bearings is extended to include static and dynamic loadings as well as shaft orbits and critical speed and damping information (Humphris et al., 1989). This enhances their use as diagnostic and preventative maintenance tools which are built into machinery and can be used on line.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):789-794. doi:10.1115/1.2920694.

Algorithms developed by the authors in previous work (Azarkhin and Richmond, 1990; Azarkhin and Richmond, 1991) have been used here to model friction due to ploughing of rigid, adhesionless, fully embedded asperities through the surface of a material undergoing bulk plane strain deformation. It is shown that the mean frictional stress is influenced by the intensity of the subsurface deformation and by the size of the contacting area relative to asperity dimensions.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):795-804. doi:10.1115/1.2920695.

The Reynolds equation is derived for a mechanical seal in which both elements are flexibly mounted to rotating shafts. Stiffness and damping coefficients for the fluid film are calculated for the three degrees of freedom of each element based upon a small perturbation analysis. The analogous coefficients for simpler configurations (e.g., flexibly mounted rotor, flexibly mounted stator) contained in the literature are shown to be obtainable as degenerate cases of the more general results presented in this work.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):805-810. doi:10.1115/1.2920696.

In the mixed lubrication regime, where surface roughness may exceed the elastohydrodynamic film thickness, sliding micro-ehl films appear to collapse during their passage through the contact. A possible explanation for this can be found if the film is treated as a plastic solid. In this work, the collapse velocity is found by simultaneously solving the plastic extrusion equations and the elastic pressure equations for the film trapped between approaching asperities. The velocity of collapse is shown to be very sensitive to the asperity wavelength, slide-roll ratio, and the velocity profile between the sliding asperities.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):811-817. doi:10.1115/1.2920697.

A computational method for the prediction of static and dynamic characteristic data of tilting pad and fixed pad thrust bearings for high surface velocities and high thermal loads is developed and verified. Furthermore, a convenient model is presented, which allows the determination of the dynamic coefficients for the gyrating movement of the thrust collar, where it is sufficient using the purely axial dynamic single pad coefficients only. Introducing these coefficients into an accordingly modified rotor dynamics program, the lateral vibrations of a high speed rotor with sliding bearings are calculated and a considerable effect of the thrust bearings is shown. These theoretical results are also verified experimentally through vibration measurements at a high speed rotor test rig.

Commentary by Dr. Valentin Fuster
J. Tribol. 1991;113(4):819-827. doi:10.1115/1.2920698.

Averaged static and dynamic lubrication equations are derived in the general form containing anisotropic film thicknesses dependent on roughness orientation. Solving these equations lead to a presentation of the dynamic characteristics of lubricating films existing between computer flying heads and textured media. Squeeze effects owing to moving roughness accompanying high-frequency spacing variation are found to be given as a function of arithmetically averaged film thickness minus harmonically averaged film thickness. The calculation procedure using the finite element method is then presented for the averaged static and dynamic lubrication equations. Stiffness and damping coefficient are demonstrated indicating the effects of roughness orientation and roughness movement. Under the fixed static film conditions, the roughness decreases the stiffness. In contrast to this, the roughness only slightly affects the damping coefficient. Under fixed load and loading point conditions, these relationships are inversed. It is interesting to note that damping coefficients are decreased by longitudinal roughness and are increased by moving transverse roughness. The reason for this tendency is considered to be that the moving transverse roughness serves to generate the squeeze damping force.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

TECHNICAL BRIEFS

J. Tribol. 1991;113(4):828-831. doi:10.1115/1.2920699.

In the thermal analysis of an asperity on a sliding surface in frictional contact with an opposing surface, conditions are often idealized as a moving heat source. The solution to this problem at arbitrary Péclét number in terms of a singular integral is well known. In this study, closed-form solutions are found in terms of the exponential integral for high Péclét number. Fortunately, the closed-form solutions are accurate at Péclét number of order one. While several restrictions are necessary, the closed-form expressions offer considerable numerical savings relative to evaluations of the convolution integral.

Commentary by Dr. Valentin Fuster

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