Showing papers in "Journal of Tribology-transactions of The Asme in 1993"

Modified Reynolds Equation for Ultra-Thin Film Gas Lubrication Using 1.5-Order Slip-Flow Model and Considering Surface Accommodation Coefficient

Abstract: A 1.5-order modified Reynolds equation for solving the ultra-thin film gas lubrication problem is derived by using an accurate higher-order slip-flow model. This model features two key differences from the current second-order slip-flow model. One is the involvement of an accommodation coefficient for momentum. The other is that the coefficient of the second-order slip-flow term is 4/9 times smaller than that for the current model. From the physical consideration of momentum transfer, the accommodation coefficient is found to have no affect on the second-order slip-flow term. Numerical calculations using the 1.5-order modified Reynolds equation are performed

Calculation of Stiffness and Damping Coefficients for Elastically Supported Gas Foil Bearings

Abstract: The stiffness and damping coefficients of an elastically supported gas foil bearing are calculated. A perfect gas is used as the lubricant, and its behavior is described by the Reynolds equation. The structural model consists only of an elastic foundation. The fluid equations and the structural equations are coupled. A perturbation method is used to obtain the linearized dynamic coefficient equations. A finite difference formulation has been developed to solve for the four stiffness and the four damping coefficients. The effect of the bearing compliance on the dynamic coefficients is discussed in this paper.

Frictionally Excited Thermoelastic Instability in Automotive Drum Brakes

Abstract: Thermoelastic instability in automotive drum brake systems is investigated using a finite layer model with one-sided frictional heating. With realistic material properties of automotive brakes, the stability behavior of the one-sided heating mode is similar to that of the antisymmetric mode of two-sided heating but the critical speed of the former is higher than that of the latter. The effects of the friction coefficient and brake material properties on the critical speeds are examined and the most influential properties are found to be the coefficient of friction and the thermal expansion coefficient of drum materials. Vehicle tests were performed to observe the critical speeds of the drum brake systems with aluminum drum materials. Direct comparisons are made between the calculation and measurement for the critical speed and hot spot spacing. Good agreement is achieved when the critical speeds are calculated using the temperature-dependent friction material properties and the reduced coefficient of friction to account for the effect of intermittent contact.

Contact Surface Temperature Models for Finite Bodies in Dry and Boundary Lubricated Sliding

Abstract: A model is proposed for use is determining the contact surface temperature in dry and boundary lubricated sliding systems. The model uses the concepts of small scale and large scale heat flow restrictions to divide the temperature increase in a sliding contact into two contributions, a nominal surface temperature rise and a local temperature rise. The model is particularly useful in studying the slidingsurface temperature in bodies of finite thickness and in cases when the sliding contact area repeatedly sweeps over the same path on one of the contacting solids. Multiple heat sources within the real area of contact can be included, as can the effects of a cooling and/or lubricating fluid

A Numerical Analysis for Piston Skirts in Mixed Lubrication: Part II—Deformation Considerations

Abstract: 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 piton skirts and cylinder bore on piton 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 crank angle under engine running conditions. Complete distributions of the oil film thickness and elastic deformation as well as the hydrodynamic and contact pressures can also be given at any crank angle if needed

Measurement and Prediction of the Surface Temperature in Polymer Gears and Its Relationship to Gear Wear

Abstract: A design of a four square gear test rig that allows the wear of polymer and composite gears to be monitored continuously during operation is described. The wear behavior of three typical gear materials is examined and it is shown that the wear characteristics differ greatly. For Acetal there is a sharp rise in wear as the transmitted torque is increased, effectively limiting the torque that can be transmitted by an Acetal gear pair. This wear transition is shown to be associated with the maximum surface temperature of the gear reaching the melting point of Acetal

Contact Simulation of Three-Dimensional Rough Surfaces Using Moving Grid Method

Abstract: A new method for simulating dry contacts of three-dimensional rough surfaces has been developed. The present work is based upon Moving Grid Method (MGM) which greatly reduces the required computer memory size. One of the major difficulties in simulating contact problems is the huge requirement in computer Random Access Memory (RAM). The total number of nodes (N) to represent a typical three dimensional roughness topography can easily be in the order of tens of thousands. To store the corresponding deformation matrix based on conventional matrix method requires memory size in the order of N2 . The computational time necessary to construct such a matrix is also proportional to N2 . Thus a reasonable solution for the three dimensional contact problem can be difficult to obtain. In Moving Grid Method, the required storage space for the deformation matrix is reduced to the order of N. The computing time to construct the matrix is also proportional to N. The contact simulation solutions which include the asperity pressure distributions and the corresponding deformed surface profiles were calculated. The digitized surface profiles were used in the simulations. The 3-D results were compared with an existing 2-D model and the comparison showed excellent agreement.

Compliant Foil Bearing Structural Stiffness Analysis—Part II: Experimental Investigation

Abstract: This paper describes the second part of an investigation into the mechanism of deformation of the corrugated foil (bump foil) strips used in compliant surface foil bearings. In the earlier work, a theoretical model was developed to predict the structural characteristics of bump foil strips under various loads, including the effects of the friction forces between the compliant elements, local interaction forces, load distribution profiles, and bump configurations. In the experiments described here in, two-dimensional deflections of bump foils were recorded via an optical tracking system for a wide range of operating conditions to verify the feasibility of the theoretical model. Test results corroborate the theoretical model for the linear regions of load and the deflection parameters. The effects of the bearing design parameters, such as bump configuration, load profile, and surface coating and lubricant, on the structural characteristics of the bump foil strip were investigated. In addition, the source and mechanism of nonlinear behavior of the bump foil strips under light load conditions were examined, and more effective methods of achieving both Coulomb damping and optimum structural compliance were investigated. An understanding of the analytical and semi-empirical relations resulting from this work offers designers the potential for enhancing the design of high-performance compliant foil bearings.

The Role of Relative Humidity, Surface Roughness and Liquid Build-Up on Static Friction Behavior of the Head/Disk Interface

Abstract: Stiction at the head/disk interface has become one of the major concerns as smoother surfaces are required to achieve lower flying heights of magnetic heads over magnetic disks. In this paper, static friction forces on three types of disk samples with different surface roughness values were measured at various relative humidities. It was found that static friction coefficients were well correlated with total thickness of liquid (lubricant and adsorbed water) at the head/disk interface. The experimental data also agreed fairly well with the calculated values based on a proposed stiction model

Finite element analysis of grooved gas thrust bearings and grooved gas face seals

Abstract: A finite element method enabling the Reynolds equation solution for any face geometry of gas thrust bearing or of gas seal is presented. Difficulties due to thickness discontinuities are reduced by integration by parts of the terms involving derivatives. The weak form of the finite element Reynolds equation is then solved and the nonlinearity of the equation leads to the use of Newton-Raphson procedure. The process is fast convergent. The problem of oscillating solution is solved by the use of an upwind procedure. Some numerical examples show the accuracy and efficiency of the procedures. It is shown that the developed finite element program provides a numerical tool, more efficient than the method used until now, for the grooved gas seals design. 16 refs.

The Effect of Small Normal Loads on the Static Friction Coefficient for Very Smooth Surfaces

Abstract: The effect of normal loading on the static friction coefficient between smooth metallic surfaces is experimentally investigated. Normal loads in the range of 10 -3 N to 0.3N were applied to small diameter samples made of three different aluminum alloys and contacting a nickel coated surface. The tests were done under controlled humidity and clean air conditions. A dramatic increase in the static friction coefficient was observed as the normal load was reduced to its lower level. The behavior is attributed to the role played by adhesion forces which are more pronounced at small normal loads and smooth surfaces and is in agreement with recent theoretical analyses

Sliding Wear Calculation in Spur Gears

Abstract: In gear applications where precipitous tooth failure mode such asscoring or scuffing has been avoided, «normal» wear becomes a life-determining factor. In this paper, sliding wear in spur gears, including the considerations of gear dynamics and rough elastohydrodynamic lubrication, is analyzed. Formulas for equivalent wear rate and tooth wear profile along the line of action are derived. Results show that most materials are removed from both the addendum and dedendum tooth surfaces, and that the highest wear occurs at the beginning of an engagement. This high wear region corresponds to the root of the driving (pinion) teeth and the tip of the driven (gear) teeth. These analytical results correlate well with the practical evidences in AGMA documentation

Observations of Shear Localization in Liquid Lubricants Under Pressure

Abstract: A High Pressure Flow Visualization Cell has been designed and constructed to perform a fundamental investigation of the deformation behavior of liquid lubricants under lubricated concentrated contact conditions. A pressure of 0.3 GPa and a shear stress between parallel plates of about 25 MPa has been demonstrated. Time averaged velocity profiles show no continuous slip either in the bulk or at walls. Localized slip at shear bands inclined to the walls was demonstrated to occur during nonlinear shear response. The number of shear bands increases with shear rate (and shear stress) from as few as one at the onset of non-Newtonian flow until the shear region is essentially filled with bands with a spatial periodicity of 7 μm

Lubricating Grease Replenishment in an Elastohydrodynamic Point Contact

Abstract: A ball and disk apparatus was used to investigate the lubricant replenishment of an elastohydrodynamically lubricated point contact. This replenishment of the contact is crucial for building up a lubricating film. Whereas lubricating oil manages to achieve replenishment, lubricating grease appears not to achieve this, with lubricant starvation and a dramatic decrease in film thickness as a result. The distribution of grease around the contact was studied using normal and high-speed video. The movements of grease in the vicinity of the contact could be seen by adding molybdenum disulfide particles to the grease

The Contact Between Rough Surfaces With Longitudinal Texture—Part I: Average Contact Pressure and Real Contact Area

Abstract: This paper describes a model to study the contact between two purely longitudinally rough surfaces based on theparabolic indentor problem in elasticity. Rough surfaces are characterized with three parameters: rms roughness, autocorrelation length, and bearing area. Problems encountered by conventional roughness models are treated here. It is shown that the average contact pressure and real contact area obtained from this model agree very well with a computationally more intensive model developed by Lee (1989), up to the bulk yielding pressure

Application of a Mixed Lubrication Model for Hydrostatic Thrust Bearings of Hydraulic Equipment

Abstract: On mixed and fluid film lubrication the characteristics of hydrostatic bearings for hydraulic equipment are studied numerically. By applying a mixed lubrication model derived in a previous paper to the bearings, we clarify the effects of the surface roughness, eccentric or moment loads, supply pressure and speed of rotation on the friction, flow rate, and power losses. Introducing the concept of a ratio of hydrostatic balance, we show that the minimum power loss is given as the ratio becomes close to unity

A Transient Model for Micro-Elastohydrodynamic Lubrication With Three-Dimensional Irregularities

Abstract: A transient model for micro-elastohydrodynamic lubrication with three-dimensional asperities in line contacts is presented in this paper. To take into account the effect of non-Newtonian behavior of lubricant, the Ree-Eyring viscous constitutive equation is employed in deriving Reynolds equation. The numerical solution of this model is based on an implicit finite difference scheme with under relaxation. Numerical simulation results show that the pressure bump caused by an asperity or asperities depends not only on asperity height and orientation but also on asperity dimension. The increase in asperity dimension decreases the pressure bump. The decrease in load and increase in sliding speed increases pressure bump. 14 refs.

Experimental Versus Theoretical Characteristics of a High-Speed Hybrid (Combination Hydrostatic and Hydrodynamic) Bearing

Abstract: The high-speed test facility designed and installed at Texas A&M to study water lubricated journal bearings has been successfully used to test statically an orifice compensated five-recess-hybrid (combination hydrostatic and hydrodynamic) bearing for two radial clearance configurations. Measurements of relative-bearing position, torque, recess pressure, flow rate, and temperature were made at speeds from 10,000 to 25,000 rpm and supply pressures of 6.89 MPa (1,000 psi), 5.52 MPa (800 psi), and 4.14 MPa (600 psi)

Lubrication With Binary Mixtures: Liquid-Liquid Emulsion

Abstract: There are numerous instances of technical importance in which multicomponent lubricants are utilized either by design or by necessity. In many of these cases one of the components is a liquid while the other component is a gas, as in squeeze film dampers during high frequency operation, or both components are liquids, as in the oil-water emulsion used in metal forming processes. In this paper our objective is to develop a self-consistent theory of hydrodynamic lubrication with bicomponent, liquid-liquid lubricants. The basic scientific method utilized is the continuum theory of mixtures. In this, first instance we test the model on journal bearings lubricated with water-in-oil and oil-in-water emulsions.

On the Pressure Rippling and Roughness Deformation in Elastohydrodynamic Lubrication of Rough Surfaces

Abstract: The Objective of this paper is to conduct a qualitative analysis on the effects of lubricant shear thinning, lubricant shear heating and the roughness-induced transients on the pressure rippling and roughness deformation that occurs under elastohydrodynamic lubrication (EHL) conditions. To facilitate the analysis, the numerical solutions to an example problem (EHL) line contact between a perfectly smooth surface and a sinusoidal rough surface are presented. This micro-EHL problem is first solved using the conventional model of a Newtonian lubricant and a stationary rough surface under isothermal conditions

Finite Element Analysis of Elastoplastic Indentation: Part II—Application to Hard Coatings

Abstract: A finite element model previously described is used to analyze indentation of hard - face materials. The materials (substrate and coating) are supposed elastoplastic, the spherical indenter is elastic. The state of stress during indentation (including unloading) of hard-face materials (chromium layer on steel) is investigated in details. The tensile stresses which might lead to failure are especially discussed, and related with experiments showing fracture or delamination of the coating. The model also shows the influence of film thickness on surface and interface stresses

A Study of the Thermal Characteristics of the Leading Edge Groove and Conventional Tilting Pad Journal Bearings

Abstract: In this paper dealing with the tilting pad journal bearing, experimental results are presented which show that, at higher shaft speeds, the leading-edge-groove (LEG) design has significantly lower operating temperatures to those of the conventional design of tilting pad journal bearing. Subsequent theoretical analysis has shown that this reduction in pad operating temperature is the result of feeding cool oil directly to the leading edge of the pad. This has the effect of reducing the amount of hot oil carried over from one pad to the next.

Lubrication With Binary Mixtures: Bubbly Oil

Abstract: Mixtures do not exhibit Newtonian behavior even when their individual components themselves are Newtonian, and thus classical lubrication theory is not applicable to bearings lubricated with mixtures. Our objective is to extend hydrodynamic lubrication theory to lubrication with mixtures of a Newtonian liquid and an ideal gas. To this end, we make use of the theory of interacting continua and derive two coupled non-linear equations in component densities. The extended theory is tested on finite journal bearings: our results of pressure distribution show good qualitative agreement with the experimental data of Braun et al

Simultaneous pressure measurement and high-speed photography study of cavitation in a dynamically loaded journal bearing

Abstract: Cavitation of the oil film in a dynamically loaded journal bearing was studied using high-speed photography and pressure measurement simultaneously. Comparison of the visual and pressure data provided considerable insight into the occurrence and nonoccurrence of cavitation. It was found that (1) for the submerged journal bearing, cavitation typically occurred in the form of one bubble with the pressure in the cavitation bubble close to the absolute zero; and (2) for cavitation-producing operating conditions, cavitation did not always occur; with the oil film then supporting a tensile stress.

Tribology of Ion Bombarded Silicon for Micromechanical Applications

Abstract: Silicon is used in the fabrication of microelectromechanical systems (MEMS). The friction and wear characteristics are of major design concern for any mechanical device requiring relative motion. In the present investigations we have studied the influence of ion bombardment on the microstructure, crystallinity, composition, microhardness, friction, and wear behavior. The ion bombardment modifies the elastic/plastic deformation characteristics and crack nucleation that occurs during the indentation. C+ bombarded monocrystalline and polycrystalline Si exhibit very low coefficient of friction (0.025–0.05) and wear factors (10−7 mm3 /N m) while slid against 52100 steel and alumina in dry and moist air and dry nitrogen atmospheres. Ion bombardment resulted in the formation of an amorphized layer that consists of SiC, C, and Si. We have shown that the improvements in friction and wear are because of the formation of SiC and not because of amorphization alone.

Three-dimensional temperature distribution in EHD lubrication. II. Point contact and numerical formulation

Abstract: A numerical study of Newtonian thermal elastohydrodynamic lubrication (EHD) of rolling/sliding point contacts has been conducted The two-dimensional Reynolds, elasticity and the three-dimensional energy equations were solved simultaneously to obtain the pressure, film thickness and temperature distribution within the lubricant film The control volume approach was employed to discretize the differential equations and the multi-level multi-grid technique was used to simultaneously solve them The discretized equations, as well as the nonorthogonal coordinate transformation used for the solution of the energy equation, are described The pressure, film thickness and the temperature distributions, within the lubricant film at different loads, slip conditions and ellipticity parameters are presented 20 refs

A Direct Analysis of Three-Dimensional Elastic-Plastic Rolling Contact

Abstract: A novel treatment of a direct procedure for elastic-plastic analysis and shakedown is presented and its application to problems in three-dimensional rolling contact with or without case-hardened layers is demonstrated. The direct approach consists of an operator split technique, which transforms the elastic-plastic problem into a purely elastic problem and a residual problem with prescribed eigenstrains. These eigenstrains are determined using an incremental projection method based on the purely elastic solution and a special representation of the yield condition for a linear-kinematic hardening material. The three-dimensional residual problem is then further split into a plane problem and an anti-plane problem which are readily solved using the finite element method. A significant advantage of the present analysis over the alternative approach of simulating repeated rolling until shakedown occurs is that in the present analysis, the final shakedown solution is obtained directly by solving three elasticity problems. Results are compared with full elastic-plastic finite element calculations available from the literature and good agreement is observed. The effects of surface hardened layers on the distributions of residual stress and displacement are investigated for both two- and three-dimensional contact. The direct approach is shown to be a straightforward and efficient method for obtaining the steady state solution in the analysis of three-dimensional problems in rolling and/or sliding contact

Analysis of Lubrication Theory for the Power Law Fluid

Abstract: A lubrication theory for the power law fluid is developed and analyzed. Only the infinite width gap is considered. Considered is flow between rigid walls of arbitrary shape under combined Couette and squeezing motion with a pressure gradient. equations appropriate to a thin film are derived by asymptotic integration of the three-dimensional equations of fluid mechanics. Further integration of these equations yields an algebraic equation for the pressure gradient. Working out the details of the structure of the equation enables us to develop a numerical algorithm for its solution

Competition Between Fatigue Crack Propagation and Wear

Abstract: Based on a semi-empirical derivation of the Paris fatigue law, the fatigue crack length a is related to the yield limit or flow stress, which ultimately is related to the hardness of the material. The analysis considers together the cyclic loading, which tends to increase the surface crack length, and the wear, which tends to decrease the crack length at the surface, and shows that under certain conditions a stable crack length may be developed. Experiments conducted on two test groups ((i) Rc = 58.5 and (ii) Rc = 62.7) tend to support the present analysis.

Temperature Rise at the Sliding Contact Interface for a Coated Semi-Infinite Body

Abstract: In this paper, a three-dimensional model of a semi-infinite layered body is used to predict steady-state maximum surface temperature rise at the sliding contact interface for the entire range of Peclet number. A set of semi-empirical solutions for maximum surface temperature problems of sliding layered bodies is obtained by using integral transform, finite element, heuristic and multivariable regression techniques. Two dimensionless parameters, A and Dp, which relate to coating thickness, contact size, sliding speed and thermal properties of both coating and substrate materials, are found to be the critical factors determining the effect of surface film on the surface temperature rise at a sliding contact interface