Hydrodynamic Lubrication Model Research Articles

Shear thinning and frequency dependent behaviour of adsorbed polymer layers: Part I. Experimental aspects and a first order analysis

Nanorheological measurements were carried out using an oscillatory AFM technique to investigate the viscoelastic properties of adsorbed hydroxypropyl guar (HPG) layers. The oscillations were performed at frequencies between 300 Hz and 1 kHz, with applied oscillation amplitudes of 2 nm. Qualitative data analysis was carried out using complex viscosity and complex modulus transfer functions based on a hydrodynamic lubrication model. The results indicated viscous behaviour at large surface separations and viscoelastic behaviour in the region of polymer layer overlap, as would be expected for adsorbed polymer layers. However, the adsorbed HPG layers also showed an indication of frequency dependent viscoelastic behaviour and shear thinning (reduction of viscosity with frequency). Furthermore, there appeared to be an unanticipated correlation between the apparent thickness of the adsorbed layers and the viscoelastic properties of the system, which may be attributed to the shear thinning behaviour of the layers.

Existence and uniqueness for a non-coercive lubrication problem

The purpose of this paper is to study a mathematical model of hydrodynamic lubrication when cavitation takes place. The obtained equation is a non-linear degenerate partial differential equation.

Probabilistic and sensitivity analyses for the performance characteristics of the main bearings in an operating engine due to variability in bearing properties

Surrogate models (metamodels) are developed and used to evaluate an engine bearing performance and perform probabilistic sensitivity analyses. The metamodels are developed based on results from a simulation solver computed at a limited number of sample points. An integrated system-level engine simulation model, consisting of flexible crankshaft and block dynamic models, connected by a detailed hydrodynamic lubrication model, is employed for constructing the metamodels. An optimal symmetric Latin hypercube sampling algorithm is utilised. The metamodels are employed for performing probabilistic and sensitivity analyses. The initial clearance between the crankshaft and each main bearing and the oil viscosity comprise the random variables. The maximum oil pressure and the percentage of time (time ratio) within each cycle that a bearing operates with oil film thickness less than a user defined threshold value at each main bearing constitute the system performance variables.

A finite element model for hydrodynamic lubrication of cold extrusion with frictional boundary condition

In this paper, based on elastic–plastic hydrodynamic lubrication theory and metal-forming mechanism, a model of hydrodynamic lubrication during cold extrusion is established. The frictional boundary condition during rigid-plastic finite element simulation of cold extrusion is dealt with using the proposed model. In addition, the distribution of strain in the billet during cold extrusion is analyzed by FEM. The numerical result is discussed and compared with the experimental result.

The half-wetted bearing. Part 2: Potential application in low load contacts

In a companion paper (Part 1) a hydrodynamic lubrication model was developed to describe the flow and pressure in a bearing in which the lubricant has a no-slip boundary condition with one bearing surface but can slip against the other surface at a critical shear stress. This paper examines the current evidence for liquid slip at solid surfaces and outlines the problems inherent in the lubrication of low load contacts. The paper then shows that a bearing design in which one surface is very smooth and oleophobic, thereby allowing lubricant slip to occur, while the other surface is conventionally oleophilic, may provide a very low friction coefficient in low load conditions such as are present in microelectromechanical systems and hard disk drives.

Effect of Dissimilar Interfacial Roughness Properties on Deformation Characteristics of Plastic Compression

A thermoelastic-plastic coupling formulation of large deformation combining with a hydrodynamic lubrication model is proposed to analyse the plastic upsetting of a cylinder, accounting for dissimilar interface conditions. The flow stress of the deforming workpiece is considered as a function of strain, strain rate and temperature; the lubrication model involves different lubrication regions from the thick film region at one extreme to the boundary lubrication region at the other. The effects of unequal interface frictional constraints, resulting from dissimilar interfacial roughness properties, at the top and bottom end surfaces on the temperature, strain component and effective strain distributions are investigated. The asymmetrical material flow inducing an uneven billet profile, together with the variations in the top and bottom die surface loads, are also predicted. The results obtained are consistent with the observations of upsetting experiments.

Investigation of Die-Workpiece Interface Friction with Lubrication During the Upsetting Process

A thermo-elastic plastic model of a large deformation combined with a hydrodynamic lubrication model is developed in this paper. The former formulation solves the interaction between mechanical load and thermal load using the finite-element method and the finite-difference method in which the flow stress is taken as a function of strain, strain rate and temperature. While the latter one accounts for the different lubrication regions which may occur at different areas of the die-workpiece interface or at different times, and in which the full film lubrication and the mixed and boundary lubrication conditions are included. Thus, a realistic deformation behaviour can properly be modelled. The calculated forging load and the deformed shape of the workpiece are in good agreement with the results obtained from the upsetting experiment.

Elastohydrodynamic Analysis of the Sealing Performance of Rotary Shaft Helix Lip Seals—Part 1

Based upon EHD theory, the sealing performance of a rotary shaft helix lip seal has been analyzed numerically using a complete hydrodynamic lubrication model. In order to verify the analytical method, several experiments are carried out under different operating conditions. After verification by the experimental results, the analytical method is used to calculate the sealing limit and the optimum seal radial load. The effects of the boundary pressure of sump side upon the pumping rate of a seal are discussed.

Effects of Surface Texture on Hydrodynamic Lubrication of Dynamically Loaded Journal Bearings

The effects of two-sided purely longitudinal, transverse and isotropic surface roughness on the hydrodynamic lubrication of dynamically loaded finite journal bearings are analyzed using Christensen's stochastic model of hydrodynamic lubrication of rough surfaces and considering running-in effect on roughness height distributions. A detailed study of the above system in terms of the nominal minimum film thickness and the maximum film pressure demonstrates that the effects of roughness are closely tied to the roughness texture and structure, features of nominal geometry, and operating factors.

A hydrodynamic lubrication model for the deep‐drawing process

AbstractA steady hydrodynamic lubrication model that includes the pressure viscosity factor has been developed for the deep‐drawing process. Equations for lubricant film thickness, radial and drawing stresses are presented. Analysis reveals that the pressure viscosity factor has a significant influence on estimating lubricant film thickness and radial and drawing stresses.

Refined Models for Hydrodynamic Lubrication in Axisymmetric Stretch Forming

Two mathematical models for axisymmetric stretch forming with a spherical punch are developed. The models combine a finite element representation of the sheet deformation with a hydrodynamic lubrication model. In one model the influence of sheet bending stiffness is taken into account while in the other only the membrane stiffness is considered. Comparison of the predictions of the models with the film thickness measurements of Hector and Wilson indicates that the inclusion of elastic effects is important in predicting lubricant film thickness. The results of the bending model are in particularly good agreement with the experimental data. A useful analytical method for predicting the film thickness at the center of the conjunction at the onset of yield is also developed.

Isoviscous Hydrodynamic Lubrication of Deep Drawing and Its Comparison With Experiment

An analytical model for the isoviscous hydrodynamic lubrication of deep drawing is developed. The model covers the complete drawing stages from sheet metal blank to the drawn cup-shaped product. Equations to calculate the film thickness, radial, and drawing stresses related to the blank holder squeezing action are presented. Theoretical predictions of both film thickness and drawing force ratio for lubricated, low carbon steel are compared with experimental measurements.

Boundary and hydrodynamic lubrication

Models of typical characteristics of the surfaces of two interfacing solids under pressure and sliding against each other are described. In the first model, the asperities, wedges of the harder surface, indent into the softer surface due to the applied pressure, producing opposing ridges on the surface of the softer component. The gap between the opposing asperities is filled with liquid, establishing boundary lubrication. As sliding is maintained, the ridges are mobilized and an eddy flow is established in the trapped lubricant. The power required to mobilize the ridges and to establish eddy flow in the lubricant is calculated and thus the friction resistance to sliding is determined. The pressure generated in the liquid due to shear is also evaluated. It becomes clear that the height of the ridge due to indentation is inversely proportional to the speed of sliding. The higher the sliding speed, the higher is the liquid pressure that is countering the loading pressure and the smaller is the indentation. At high enough speed (to be replaced in due course by the Sommerfeld number), the entire load is supported by the pressure generated in the liquid, indentation is eliminated and hydrodynamic lubrication commences. The classical model for hydrodynamic lubrication where two inclined surfaces slide against each other is described. The gap between the two surfaces ϵ min at their closest point is a monotonically increasing function of Sommerfeld number S. The resistance to sliding, established through the shear in the liquid, determines the friction valve. This model leads directly to the characteristics where for diminishing values of Sommerfeld number the resistance to sliding is proportional to the pressure (τ = μp) and the proportionality factor is equal to the tangent of the angle of inclination (μ= tan α). The increase in friction with increasing values of Sommerfeld number is also determined. Combining the two models, one notices that at low speed and Sommerfeld number, the liquid pressure is not sufficient to float the two surfaces and indentation prevails, with boundary lubrication. With increasing speed (Sommerfeld number), the height of the ridge (by the first model) decreases. When it diminishes to values lower than those predicted for the gap between the surfaces in the second model for the same speed, the boundary lubrication ceases and hydrodynamic lubrication commences.

Modelling the effect of lubrication on friction behaviour

AbstractModels of typical characteristics of the surfaces of two solids interfacing one another under pressure and sliding with respect to each other are described in Models 1 (Figure 1) and 2 (Figure 2). In Model 1 (Figure 1) the asperities, wedges of the harder surface indent into the softer surface due to the applied pressure, thus producing opposing ridges on the surface of the softer component. The gap between the opposing asperities is filled with liquid, establishing boundary lubrication. As sliding is maintained, the ridges are mobilized and an eddy flow is established in the trapped lubricant. The power required to mobilize the ridges and to establish eddy flow in the lubricant is calculated and thus the friction resistance to sliding is determined. Simultaneously, the pressure generated in the liquid due to shear is also evaluated. It becomes clear that the height of the ridge due to indentation is inversely proportional to the speed of sliding. The higher the sliding speed, the higher is the liquid pressure that is countering the loading pressure and the smaller is the indentation. At a high enough speed (to be replaced in due course by the Sommerfeld Number) the entire load is supported by the pressure generated in the liquid, indentation is eliminated and hydrodynamic lubrication commences. The classic model for hydrodynamic lubrication where two inclined surfaces glide atop each other is described in figure 2. Here the gap between the two surfaces (q.J a t their closest point is a monotonically increasing function of Sommerfeld Number (S). The resistance to sliding as established through the shear in the liquid determines thefriction value. This model leads directly to the characteristic of Coulomb or Emontons where for diminishing values of Sommerfeld Number the resistance to sliding is proportional to the pressure (τ = μp) and the proportionality factor is equal to the tangent of the angle of inclination (μ = tana). In the present work, the increase infnction with increasing values of the Sommerfeld Number is also determined. Combining the two models one notices that, a t low speed and Somrfeld Number values, the liquid pressure is not sufftcient tofloat the two surfaces and indentation prevails together with boundary lubrication. With increasing speed (Sommerfeld Number) the height of the ridge (by Model 1) decreases, and when it diminishes to values lower than those predicted for the gap between the surfaces in the second model for the same speed, the boundary lubrication ceases and hydrodynamic lubrication commences.

On the Lubrication of Rough Rollers

Christensen’s stochastic model of hydrodynamic lubrication as extended to two sided roughness is used to study the effect of surface roughness in the analysis of lightly loaded rollers in combined rolling, sliding and normal motion. A detailed study of the above system in terms of dimensionless parameters, Q (involving the normal and entraining velocity, the minimum film thickness and the equivalent cylinder radius); the slide roll ratio and the surface roughness parameter is made for purely longitudinal and purely transverse surface roughness.

An Automotive Piston Lubrication Model

An analytical study of the dynamics of a piston in a reciprocating engine was conducted. The analysis, which incorporates a hydrodynamic lubrication model, was applied to a V-8 automotive spark ignition engine. The variation of piston transverse position and rotation with crank angle, and the piston-skirt frictional power loss were calculated for different wrist pin locations, piston-to-cylinder clearances, and lubricant viscosities. The results obtained indicate that piston motion is strongly affected by the location of the wrist pin and that piston-skirt friction is increased significantly if the wrist pin is at an unfavorable position. In addition, piston dynamics were found to be sensitive to piston-cylinder bore clearance and lubricant viscosity, underscoring their importance in engine design. Presented at the 37th Annual Meeting in Cincinnati, Ohio, May 10–13, 1982

A Refined Analytical Model for Hydrodynamic Lubrication of Cold Extrusion and Its Comparison With Experiment

In a refined analytical model for the hydrodynamic lubrication of cold extrusion, effects of viscous heating in the inlet zone and surface temperature in the work zone are included to estimate extrusion pressure for both unsteady and steady lubrication. An experimental study indicates that a hydrodynamic lubricant film may be formed by reducing friction at the start of extrusion by a secondary lubricant. Theoretical estimation of unsteady extrusion pressure is in agreement for extrusion of aluminium billets lubricated with castor oil.

A Simple Low Deborah Number Model for Unsteady Hydrodynamic Lubrication, Including Fluid Inertia

In unsteady hydrodynamic lubrication the film thickness varies with time, producing the squeeze film term in the Reynolds equation, where the fluid is assumed to be Newtonian and fluid inertia effects are neglected. A Deborah and Reynolds number perturbation solution correction to lubrication theory is presented which can accommodate arbitrary smooth two‐dimensional surface geometry and arbitrary time variation in film thickness. The constitutive equation used is one recently proposed by Harnoy in which a new type of material derivative is used allowing separate consideration of relaxation and normal stress effects, each governed by a separate material parameter. A low Deborah number expansion is developed to obtain a simple two‐parameter (viscosity and relaxation time) stress‐explicit relation. Corrections to the lubrication theory for inertia and viscoelastic effects in terms of Reynolds and Deborah numbers are presented. Solutions to several problems are presented: (1) parallel surfaces with constant a...