Contact Elastohydrodynamic Lubrication Research Articles

Lubricant Rupture Ratio at Elastohydrodynamically Lubricated Contact Outlet

Elastohydrodynamically lubricated (EHL) contacts rarely exist as single contacts. Multiple contacts or single contacts subjected to the repeated over-rolling represent more often the case in practical applications. A typical example is the rolling element bearing. A lubricant rupture mechanism at each contact outlet determines the lubricant availability to the succeeding contact. This work presents a quantitative description of the lubricant film thickness rupture in EHL contact outlet with the use of the fluorescent microscopy. A rupture ratio of the film thickness between two diverging surfaces exiting the contact was measured for both pure rolling and rolling–sliding conditions. The influence of variation of several parameters such as lubricant properties, rolling speed or rolling element ellipticity to the lubricant rupture ratio was investigated. Understanding of the physical phenomena of the lubricant rupture extends further possibilities in both experimental and theoretical researches of the starved EHL.

Influence of thermo-mechanical properties of coatings on friction in elastohydrodynamic lubricated contacts

This paper presents a numerical investigation of the influence of thermo-mechanical properties of coatings on friction in elastohydrodynamic contacts. In a previous work by the author, it was shown that thermal properties of coatings had a significant influence on friction. In fact, under high sliding speeds, friction was found to increase with the thermal inertia of coatings. The current work reveals that mechanical properties of coatings also have a significant impact on friction. Friction actually exhibits an increase with the rigidity of the coating. Furthermore, a combination of soft coatings with low thermal inertia is shown to maximize friction reduction while hard coatings with high thermal inertia maximize friction increase. These effects are found to increase with the coating thickness.

Uniform Equations in the Inlet and Exit Zones of Heavily Loaded Point and Line Elastohydrodynamically Lubricated Contacts Involved in Various Steady Motions

Heavily loaded point elastohydrodynamically lubricated (EHL) contacts involved in steady purely transitional, skewed transitional, and transitional with spinning motions are considered. It is shown that in the central parts of the inlet and exit zones of such heavily loaded point EHL contacts the asymptotic equations governing the EHL problem along the lubricant flow streamlines for the above types of contact motions can be reduced to two sets of asymptotic equations: one in the inlet and one in the exit zones. The latter sets of equations are identical to the asymptotic equations describing lubrication process in the inlet and exit zones of the corresponding heavily loaded line EHL contact (Kudish, I. I., 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman and Hall/CRC). For each specific motion of a point contact, a separate set of formulas for the lubrication film thickness is obtained. For different types of contact motions, these film thickness formulas differ significantly (Kudish, I. I., 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman and Hall/CRC). For heavily loaded contacts, the discovered relationship between point and line EHL problems allows to apply to point contacts most of the results obtained for line contacts (Kudish, I. I., 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman and Hall/CRC; Kudish, I. I., and Covitch, M. J., 2010, Modeling and Analytical Methods in Tribology, Chapman and Hall/CRC).

On the compressive heating/cooling mechanism in thermal elastohydrodynamic lubricated contacts

The importance of compressive heating/cooling occurring within lubricating films in thermal elastohydrodynamic lubricated contacts has not been given sufficient attention in the literature. This paper presents a numerical investigation of this mechanism and attempts to quantify its importance as compared to shear heating under pure-rolling and rolling–sliding conditions. It is found that even under pure-rolling, compressive heating/cooling remains in most cases less important than shear heating or at best, of the same order. Under rolling–sliding conditions, as soon as the slightest sliding occurs, heat generation is governed by shear heating. The dependence of compressive heating/cooling on operating conditions is also examined. Finally, the impact of this mechanism on the lubricating performance of these contacts is considered under various operating conditions.

A Dichromatic Interference Intensity Modulation Approach to Measurement of Lubricating Film Thickness

The study aims to extend the measurement range of dichromatic interferometry in lubricating film thickness measurement. Subtraction of two sets of interference fringes, which are produced by dichromatic (red and green) lights, gives a modulated signal of intensity against film thickness. The measuring range without wavelength ambiguity is limited to the first half-cycle of the beat wave in the modulated signal. Theoretical and experimental analyses of the modulated interference intensity variation against film thickness were conducted. The differences in the pattern of the modulated interference intensity were obtained in the first three half-cycles of the beat wave. Based on that, a robust dichromatic interference intensity modulation approach for lubricating film measurement was derived and its measuring range without wavelength ambiguity was successfully extended to the magnitude equivalent to three half-cycles of the beat wave. To test the feasibility and credibility of this approach, the film thickness in elastohydrodynamic and hydrodynamic lubricated contacts was measured. The results were well correlated with the classical theory. Using red and green lasers with wavelength of 653 and 532 nm, respectively, the measurement range can be extended to 4 μm.

Effects of Skewed Surface Textures on Lubricant Film Thickness and Traction

The effects of surface texture skewness (Ssk) on lubricant film thickness and traction were investigated for elastohydrodynamic lubrication (EHL) contacts. This was accomplished by analyzing three-dimensional simulated surface textures with EHL computational modeling and then verifying the results with rotating ball-on-disk traction experiments. EHL modeling was used to identify critical values for surface roughness average (Sa) and skewness (Ssk) corresponding to a stable lubricant film formation. The critical values were then used to specify test specimen textures that were fabricated for traction experiments. The results from EHL modeling and traction experiments suggest that surfaces with individual skewness Ssk values ranging from −0.4 to −2.2 at constant roughness Sa do not yield significant differences in lubricant film thickness or measured traction. Surfaces with extreme negative skewness Ssk values (approximately −4.7 or lower) may yield significant differences in contact pressure and lubricant film thickness.

Multiple Inhomogeneous Inclusions and Cracks in a Half Space Under Elastohydrodynamic Lubrication Contact

A semi-analytic solution is presented for multiple inhomogeneous inclusions and cracks in a half-space under elastohydrodynamic lubrication contact. In formulating the governing equations, each inhomogeneous inclusion embedded under the contacting surfaces is modeled as a homogeneous inclusion with initial eigenstrains plus unknown equivalent eigenstrains by employing Eshelby's equivalent inclusion method, while each crack of mixed modes I and II is treated as a distribution of climb and glide dislocations with unknown densities according to the dislocation distribution technique. Such a treatment converts the problem into a homogeneous lubricated contact with disturbed deformation due to the inclusions and cracks. The unknowns in the governing equations are integrated by a numerical algorithm and determined iteratively by utilizing a modified conjugate gradient method. The iterative process is performed until the convergence of the half-space surface displacements, which involve the displacements due to the inhomogeneous inclusions and cracks as well as the fluid pressure. Samples are presented to demonstrate the generality of the solution.

Analysis of fluid pressure, interface stresses and stress intensity factors for layered materials with cracks and inhomogeneities under elastohydrodynamic lubrication contact

This study conducts investigations on coated materials with subsurface inhomogeneities and cracks under lubricated contact. The analytical elastic solution of cracked materials with inhomogeneities subjected to elastohydrodynamic lubrication contact is employed by modeling the topmost coating as an inhomogeneity of finite size. The interactions between the loading body, the fluid lubrication film, the coating/substrate system and the subsurface micro-defects within the system are taken into account. The effects of coatings and subsurface defects on the lubricant film thickness and fluid pressure profiles and elastic fields are analyzed in the cases presented. Stress intensity factors for the embedded cracks are obtained based on the solution and involved in the analysis.

Comment on Šperka, P., I. Křupka, M. Hartl (2014). “Evidence of Plug Flow in Rolling–Sliding Elastohydrodynamic Contact.” Tribology Letters 54(2): 151–160

The authors were excited to see the recent paper by Sperka et al. (2014) as it seems to confirm recent findings in our own recent works [1–3]. The plug flow mechanism is important to explain the traction in elasto-hydrodynamic lubrication (EHL) contacts with and without nanoparticles. Although in our paper we do not explicitly call the mechanism plug flow for the case without particles, we do show that there is localized shear near the surfaces. This is essentially the same mechanism and just described differently. The presence of nanoparticles can further enhance the effect by forcing an intermediate lubricant layer to follow the nanoparticle as a plug. Using molecular dynamics, we showed that this could happen with and without the nanoparticles (i.e., for conventional fluids or lubricants and nanofluids), if the film is sufficiently thin. The authors originally investigated this when our experimental measurements with the nanofluid resulted in friction coefficients that were lower than expected in the EHL regime. There are also other differences between the work by Sperka et al. (2014) and ours. For instance, they use the particles in a controlled experiment to trace the velocity profile, while in our paper, the particles enhance the mechanism. The geometry, surface material, lubricant composition, and operating conditions may also be different between the two works, but the observed mechanism is still very similar.

Localized Boundary Effect on Elastohydrodynamic Lubricated Film Shape

The study aimed to determine the formation of an adsorption film at elastohydrodynamic lubricated (EHL) contacts and its effects on EHL film shape and friction. Experiments were conducted on an optical EHL test rig with surfaces of different surface energies. A new type of “abnormal” EHL film shape characterized with three dimples in the inlet of the contact was obtained in pure ball sliding experiments with long-chain polybutene. The adsorption layer was inferred to be the main cause for the “tri-dimple” phenomenon. The “tri-dimple” formation was examined. Under a fixed speed, a single inlet dimple gradually broke into three dimples with increasing number of ball rotation, and it happened with slight increase in friction force. Three zones, namely a central and two lateral zones, of the contact were classified and characterized with different levels of influence on the adsorption layer.

Molecular interaction originating from polar functional group in lubricants and its relationship with their traction property under elastohydrodynamic lubrication

AbstractThe correlation between molecular interaction and traction properties was investigated using a traction tester and in situ observation of elastohydrodynamic lubrication film with a micro‐Fourier transform infrared spectrometer. The sample oils used were polypropylene glycols (PPGs) with the end‐group of alcohol or ether and a synthetic hydrocarbon oil, poly‐α‐olefin. From the traction tests, it was found that the traction coefficient of PPG was sensitive to the end‐group. PPG with alcohol as the end‐group showed a higher traction coefficient than that with the ether group. In situ observation with a micro‐Fourier transform infrared was performed in order to investigate the molecular interaction of the lubricant oil. It was found that the hydrogen bonding of hydroxyl groups in PPG was strengthened by high pressure in the Hertzian contact region. These results suggest that the rheological properties in the elastohydrodynamic lubrication contact region were affected by the strengthened hydrogen bonding. Copyright © 2014 John Wiley & Sons, Ltd.

Occurrence of High Pressure Spike in Unidirectional Start–Stop–Start Point Contacts

The transient film thickness and pressure distributions in point elastohydrodynamic lubrication (EHL) contacts during start–stop–start motion are discussed based on experimental and numerical analyses. When the machine element starts to move after the stopping, where the oil is entrapped between two surfaces, the pressure at the exit area increases very much. The pressure increase depends markedly on the overall film thickness before the stopping of the motion, but is hardly controlled by the acceleration after the stopping. It can be considered that this phenomenon affects the rolling contact fatigue damage.

Elastohydrodynamic lubrication modeling for materials with multiple cracks

This paper presents a semi-analytic solution for multiple cracks beneath a half-space surface under elastohydrodynamic lubrication (EHL) contact. The solution not only takes into account the fluid-structure interactions in the EHL contact but also the interactions among all the cracks. In developing the governing equation, each crack of mixed modes I and II is modeled as a continuous distribution of climb and glide dislocations with unknown densities. With such a treatment, the original problem for materials with multiple cracks is converted into two subproblems: a homogeneous EHL contact problem with the fluid pressure distri- bution and the lubricant film thickness to be determined, and a half-space problem with unknown dislocation densities, which are iteratively obtained by a modified conjugate gradient method. A numerical algorithm is developed to integrate the two problems. The computational process is performed until the convergence of the displacements, which are the sum of the displacements due to the fluid pressure and the subsurface cracks. Sample cases are presented to analyze the pressure and lubricant film thickness profiles of EHL contact and the subsurface stresses for cracked materials.

Elastohydrodynamic Lubrication Model With Limiting Shear Stress Behavior Considering Realistic Shear-Thinning and Piezo-Viscous Response

This paper addresses a largely ignored aspect pertaining to the elastohydrodynamic lubrication (EHL) traction behavior of fragile lubricants which undergo transition to glassy state at typical EHL contact zone pressures. For such lubricants, a conventional EHL model predicts extremely high and unrealistic values of traction coefficient, especially under near pure rolling conditions where thermal effect is negligible. Therefore, an EHL model incorporating the effect of limiting shear stress and the associated wall slip phenomenon is presented herein. Unlike the other such investigations involving limiting shear stress behavior, the present model employs Carreau-type power-law based models to describe the rheology of lubricants below the limiting shear stress along with realistic pressure-viscosity relationships (WLF and Doolittle-Tait). The use of Carreau-type shear-thinning model in this analysis allows the simultaneous prediction of minimum film thickness and traction coefficient for lubricants which shear-thin in the inlet zone and exhibit limiting shear stress behavior in the contact zone, a feature absent in the existing EHL models utilizing ideal visco-plastic or some other unrealistic rheological model. Using published experimental data pertaining to the shear-thinning and pressure-viscosity response of two fragile lubricants (L100 and LVI260), it has been demonstrated that the present model can explain the appearance of plateau in the experimental traction curve. Also, the influence of shear-thinning parameters and the pressure-viscosity coefficient on the predicted limiting shear stress zone has been studied.

Application of Dang Van criterion to rolling contact fatigue in wind turbine roller bearings under elastohydrodynamic lubrication conditions

A 2D plane strain finite element program has been developed to investigate very high cycle fatigue in wind turbine roller bearings due to rolling contact. Focus is on fatigue in the inner ring, where the effect of residual stresses and hardness variation along the depth is accounted for. Both classic Hertzian and elastohydrodynamic lubrication theories have been used to model the pressure distribution acting on the inner raceway and results are compared according to the Dang Van multiaxial fatigue criterion. The contact on the bearing raceway is simulated by substituting the roller with the equivalent contact pressure distribution. The material used for the simulations is taken to be an AISI 52100 bearing steel and linear elastic behavior is here assumed. The effect of different residual stress distributions is also studied, as well as the effect of variable hardness along the depth, relating its values to the fatigue limit parameters for the material. It is found that both for Hertzian and elastohydrodynamic lubrication contacts, the Dang Van criterion predicts that fatigue failure will first occur in the subsurface region and that, regardless of the specific pressure distribution used, the hardness distribution can have a significant influence on the safety against failure for bearings subjected to very high cycle fatigue loading.

Asymptotic analysis of a lubricated heavily loaded spinning and rolling ball in a parabolic raceway

In the paper, the previously developed asymptotic approach to solution of the steady isothermal problem of elastohydrodynamic lubrication (EHL) for heavily loaded point contacts is applied to a lubricated point contact with rolling and spinning. It is shown that the whole contact region can be subdivided into three subregions. The central region can be subdivided into the Hertzian region and two adjacent boundary layers — the inlet and exit zones. The main results of the paper are threefold: (i) it is shown that in the central parts of the inlet and exit zones, the mechanisms and the equations controlling the behaviour of the lubrication contact parameters in heavily loaded point and line EHL contacts are identical, (ii) asymptotically precise formulas for the central and exit lubrication film thickness for pre-critical and over-critical starved and fully flooded lubrication regimes are analytically derived, and (iii) the inlet and exit zone asymptotically valid equations are uniform across all steady heavily loaded line and point EHL contacts for lubricants with the same rheology. These asymptotically valid equations were analysed and numerically solved in previously published work based on the stable methods utilising the specific regularisation approach developed for lubricated line contacts. Cases of pre-critical and over-critical lubrication regimes are considered. The formulas for the lubrication film thickness for pre-critical and over-critical starved and fully flooded lubrication regimes allow for simple analysis of the film thickness as a function of spinning angular speed, angle of the entrained lubricant and other pertinent contact characteristics. Copyright © 2013 John Wiley & Sons, Ltd.

Reduced order finite element model for elastohydrodynamic lubrication: Circular contacts

This paper presents an extension of the reduced order finite element model to the case of circular elastohydrodynamic lubricated (EHL) contacts under isothermal Newtonian considerations. The line contact model was developed and validated in a previous work (Advances in Engineering Software, 2013; 56:51−62). The model is based on a finite element discretization of the EHL equations: Reynolds, linear elasticity and load balance with a reduced order model for the linear elasticity part. All equations are solved simultaneously in a fully-coupled framework using a damped-Newton procedure allowing fast convergence rates for the global solution. This model combines fast convergence rates, reduced memory requirements and negligible model reduction errors compared to the full model which makes it an attractive tool for EHL contact performance prediction.

On the Lubricating Mechanism of Roller Skew in Cylindrical Roller Bearings

Skewing is the motion of a roller as it turns about an axis normal to the roller–race interface in cylindrical roller bearings. With a special coordinate transformation technique, complete numerical solutions for the finite line elastohydrodynamic lubrication (EHL) contact formed between a roller and races were obtained to investigate the lubricating mechanism of roller skew. The effects of skew angle, rotational speed, applied load, length of the roller, and radius of the outer race on the lubricating performance of skewed roller contact in rolling bearings is discussed. In addition, in order to weaken the end concentration of the pressure due to the skewing effect, a parabolic profile modification for the roller's generatrix was carried out. A coupled solution combining skewing and tilting effects was achieved. The results showed that when the roller is skewed, the maximum pressure appears at the end parts of the roller for a roller–outer race contact but in the middle part of the roller for a roller–inner race contact. For the roller–outer race contact, a more serious skewing effect on the lubrication can be generated by a larger skew angle, higher speed, lighter load, longer roller length, and larger radius of the outer race. The skewing effect can be reduced through the profile modification for a roller's generatrix. In general, local lubricating failure may easily occur when roller skew is coupled with the tilting effect in cylindrical roller bearings.

Asymptotic analysis of lubricated heavily loaded point contacts with skewed direction of entrained lubricant

ABSTRACTThe paper is devoted to the application of the early developed asymptotic approach to solution of the steady isothermal problem of elastohydrodynamic lubrication (EHL) for heavily loaded point contacts with skewed direction of entrained lubricant. It is shown that the whole contact region can be subdivided into three subregions: the central one, which is far away from the other two regions occupied by the ends of the horseshoe‐shaped pressure/gap distribution. The central region, in turn, can be subdivided into the Hertzian region and two adjacent boundary layers — the inlet and exit zones. Moreover, in the central region in the inlet and exit zones, the EHL problem can be reduced to asymptotically valid equations identical to the ones obtained in the inlet and exit zones of heavily loaded line EHL contacts. These equations can be analytically analysed and numerically solved on the basis of the stable methods using a specific regularization approach, which were developed for lubricated line contacts. Cases of pre‐critical and over‐critical lubrication regimes are considered. The by‐product of this asymptotic analysis is an easy analytical derivation of formulas for the lubrication film thickness for pre‐critical and over‐critical starved and fully flooded lubrication regimes. The latter allows for simple analysis of the film thickness as a function of the contact eccentricity and the direction of the entrained lubricant at the inlet in the contact. Copyright © 2013 John Wiley & Sons, Ltd.

속도의 영향에 따른 3차원 거친 표면의 혼합윤활해석

Dept. of Mechanical Engineering, Pusan National University(Received September 5, 2012 ; Revised November 11, 2012 ; Accepted November 12, 2012)Abstract − This study examined the effects of surface roughness in the mixed lubrication regime of smooth andrough surfaces for roller bearings. The average flow model was adopted for interaction between the flow rhe-ology of the lubricant and the surface roughness. The average Reynolds equation and related flow factor thatdescribes the coupled effects of surface roughness and flow rheology, the viscosity–pressure and density–pressureequations, the elastic deformation equation, and the force balance equation were solved simultaneously. Theresults showed that the effects of surface roughness on the film thickness and pressure distribution should be con-sidered, especially in elastohydrodynamic lubrication contact problems. Keywords − average Reynolds equation (평균레이놀즈방정식), flow factor (유동계수), surface roughness(표면거칠기), roller bearing (롤러베어링), dimensionless film parameter (유막계수)