Elastohydrodynamic Lubrication Film Research Articles

TVMS calculation model for gear tooth tip chipping failure with EHL

This paper proposes a calculation method for Time-Varying Mesh Stiffness (TVMS) in the presence of tooth tip chipping defects under elastohydrodynamic lubrication (EHL). A contact stiffness model for tooth tip chipping defects under EHL is established, and an analytical equation for the TVMS of chipping defects under EHL is derived. The torsional stiffness at the chipping defect under EHL is introduced, considering the influence of roughness at the chipping defect on the characteristics of the oil film and its stiffness. The effects of chipping defect size, torsional stiffness of the chipping defect under EHL, roughness, and oil film stiffness on TVMS are analyzed, providing methodological support for improving the calculation accuracy of gear TVMS.

Elastohydrodynamic Traction and Film Thickness at High Speeds

A renewed interest in elastohydrodynamic lubrication (EHL) phenomena at high speeds, for which thermal effects strongly influence both traction and film thickness, has grown out of the challenges presented by high-speed geared transmissions in electric vehicles. This study uses a new ball-on-disc set-up employing the well-known ultra-thin-film interferometry technique to simultaneously measure EHL film thickness and traction at entrainment speeds up to 20 m/s and slide-roll ratios up to 100%. The effect of fluid composition is examined for Group I, II and III mineral oils, for two polyalphaolefins in Group IV, and for the traction fluid Santotrac 50. The effect of viscosity in the range 4–180 mPa.s is investigated by varying bulk fluid temperature. At high speeds, both film thickness and traction are considerably lower than predicted by conventional EHL theory. The contact is seen to be fully-flooded for all conditions tested. The widely-used thermal EHL correction of Gupta is shown to overcorrect for the film thickness reduction even at modest SRRs. Finally, the influence of the sliding direction on traction and film thickness is discussed for this set-up, and a thermal model is proposed to explain the observed behaviour.Graphical abstract

Application of machine learning for film thickness prediction in elliptical EHL contact with varying entrainment angle

This contribution demonstrates the potential of machine learning (ML) algorithms in predicting elastohydrodynamic lubrication (EHL) film thickness in elliptical contact with varying direction of lubricant entrainment, ranging from wide to slender elliptical configurations. The input parameters pertain to worm gear contacts, which are characterized by slender-like elliptical contact between a steel and a soft metal component. The study encompasses generating a database using numerical Finite Element Method (FEM) simulations, training artificial neural network (ANN) models, and evaluating their performance in terms of bias and variance. Key outcomes include the successful training of the ANN models, detailed analysis of the impact of tailored architecture on the ANN models' performance, and the superiority of the ANN compared to other ML regression algorithms. The study further identifies key input parameters that influence prediction accuracy and introduces a strategic dataset augmentation procedure to increase local and overall prediction accuracy. This strategic dataset augmentation enhances model robustness and precision while providing insights for expanding databases collaboratively. It holds potential for broader applications of ML for performance prediction of tribological contacts, thus paving the way for advanced ML models that consider additional factors and collaborative databases refined by multiple research groups.

Electrical Impedance Spectroscopy for Precise Film Thickness Assessment in Line Contacts

In this article, we focus on utilising electrical impedance spectroscopy (EIS) for the assessment of global and contact impedances in roller bearings. Our primary objective is to establish a quantitative prediction of lubricant film thickness in elasto-hydrodynamic lubrication (EHL) and investigate the impedance transition from ohmic to capacitive behaviour as the system shifts from boundary lubrication to EHL. To achieve this, we conduct measurements of electrical impedance, bearing and oil temperature, and frictional torque in a cylindrical roller thrust bearing (CRTB) subjected to pure axial loading across various rotational speeds and supply oil temperatures. The measured impedance data is analysed and translated into a quantitative measure of lubricant film thickness within the contacts using the impedance-based and capacitance-based methods. For EHL, we observe that the measured capacitance of the EHL contact deviates from the theoretical value based on a Hertzian contact shape by a factor ranging from 3 to 11, depending on rotational speed, load, and temperature. The translation of complex impedance values to film thickness, employing the impedance and capacitance method, is then compared with the analytically estimated film thickness using the Moes correlation, corrected for inlet shear heating effects. This comparison demonstrates a robust agreement within 2% for EHL film thickness measurement. Monitoring the bearing resistance and capacitance via EIS across rotational speeds clearly shows the transition from boundary to mixed lubrication as well as the transition from mixed lubrication to EHL. Finally, we have observed that monitoring the electrical impedance appears to have the potential to perform the run-in of bearings in a controlled way.

Effects of Oil and Solid Body Temperatures on Elastohydrodynamic Lubrication Film Formation

The present study focuses on investigating the influence of oil and solid body temperatures on elastohydrodynamic lubrication (EHL) film formation. Experimental and numerical simulation methods are employed to examine three heating methods: oil and ball heating, disc heating, and entire system heating. A preliminary comparison between the measured results and numerical simulations confirms the impact of heating methods on film formation while validating the availability of the numerical models. Further numerical analysis reveals that in the case of oil and ball heating, the temperature gradient induced by differences in solid body temperatures plays a more significant role in film formation compared to the conventional thermal-viscosity wedge effect caused by EHL film shear. This effect is further amplified at large sliding–rolling ratios and in steel–steel contacts. The overall film formation is primarily governed by the oil inlet temperature, whereas local film formation characterized by a dimple shape is influenced by both thermal gradient effects and thermal-viscosity wedge effects. This study provides valuable insights for selecting appropriate heating methods in experiments as well as understanding how temperature differences affect film formation in practical engineering.

Behavior of elastohydrodynamic lubricating film point contact problems in the unsteady state of reciprocating motion

Purpose In this study a numerical analysis of the elastohydrodynamic lubrication point contact problem in the unsteady state of reciprocating motion is presented. The effects of frequency, stroke length and load on film thickness and pressure variation during one operating cycle are discussed. The general tribological behavior of elastohydrodynamic lubrication during reciprocating motion is explained. Design/methodology/approach The system of equations of Reynolds, film thickness considering surface deformation and load balance equations are solved using the Newton-Raphson technique with the Gauss-Seidel iteration method. Numerical solutions were performed with a sinusoidal contact surface velocity to simulate reciprocating elastohydrodynamics. The methodology is validated using historical experimental measurements/observations and numerical predictions from other researchers. Findings The numerical results showed that the change in oil film during a stroke is controlled by both wedge and squeeze effects. When the surface velocity is zero at the stroke end, the squeeze effect is most noticeable. As the frequency increases, the general trend of central and minimum film thickness increases. With the same entraining speed but different stroke lengths, the properties of the oil film differ from one another, with an increase in stroke length leading to a reduction in film thickness. Finally, the numerical results showed that the overall film thickness decreases with increasing load. Originality/value General tribological behaviors of elastohydrodynamic lubricating point contact, represented by pressure and film thickness variations over time and profiles, are analyzed under reciprocating motion during one working cycle to show the effects of frequency, stroke length and applied load.

Effects of a typical shear dependent viscosity on analytical elastohydrodynamic lubrication film thickness predictions: A critical issue for the classical approach

Many engineering estimates of the film thickness in the concentrated contacts of real machines have come from extrapolations of measurements of elastohydrodynamic lubrication film thickness performed in glass on steel elastohydrodynamic rigs. Such estimates are likely to have large errors due to shear dependence of viscosity. The classical film thickness formulas employed have not been validated except for some Newtonian reference liquids at room temperature because the real pressure-viscosity response measured in viscometers has been ignored. A blend of polyalpha olefin base oils with mild shear-thinning has been employed in a line contact calculation to assess the effects of shear-dependent viscosity on the power-law exponents of the classical film thickness formula. The exponents on the pressure-viscosity coefficient and on the elastic modulus of the solids are not sensitive to the non-Newtonian effect. The exponents on ambient pressure viscosity and velocity are slightly reduced by shear-thinning. The exponents on pressure and scale are substantially increased by the shear dependence. The usual practice of measuring film thickness in an elastohydrodynamic rig to obtain an effective “[Formula: see text]-value” to use in a classical Newtonian film thickness formula will overstated the film thickness of a liquid which is shear dependent in the elastohydrodynamic lubrication inlet.

Deterministic surface roughness effects on elastic material contact with shear thinning fluid media

Abstract The formation of lubrication films is described using the hydrodynamic lubrication theory, which is based on the Reynolds equation that includes shear thinning behaviors of lubricant. Contacting surfaces are considered to undergo elastic deformation owing to concentrated contact pressures that exceed 1.0 GPa in most engineering applications. Under the contact condition of a high load on a relatively small contact area, elastic deformation of contacting bodies directly influences the formation of the lubricated film. Elastohydrodynamic lubrication (EHL) analysis is applied to correctly analyze the lubricated contact. Under an EHL contact, the scale of the lubrication film thickness is frequently less than that of the surface roughness that results from either the manufacturing or running-in processes. In this work, surface roughness is considered in detail, and two-dimensional surface roughness is measured as that characterizing general engineering surface roughness. The deterministic method regarding the surface roughness is considered for computing EHL film formation under several contact conditions such as load, contact velocity, and elasticity of contacting materials.

Surface effects on elastohydrodynamic lubrication contact of piezoelectric materials with non-Newtonian fluid

Using surface piezoelectricity theory, this article investigates the elastohydrodynamic lubrication (EHL) line contact of a transversely isotropic piezoelectric half-plane with consideration of the surface effect under a rigid cylindrical punch. The surface effect in the surface piezoelectricity theory is mainly described by the following parameters: surface piezoelectric constant, surface dielectric constant, surface elastic constant, and residual surface stress. The punch is treated as an electrical insulator. The lubricant, whose viscosity and density are dependent on fluid pressure, is chosen as a non-Newtonian fluid. Firstly, by analyzing the frictionless dry contact of piezoelectric materials vith the surface effect, the dry contact pressure distribution and the EHL film thickness equation are obtained. Then, an iterative method is proposed to obtain the fluid pressure and film thickness in the lubricant contact region by calculating the fluid–solid coupled nonlinear equations. The effects of the surface dielectric constant, surface piezoelectric constant, surface elastic constant, residual surface stress, punch radius, entraining velocity, and slide/roll ratio on the film thickness and fluid pressure are examined. Our analysis indicates that the surface effect has an essential effect on the EHL contact behavior of piezoelectric materials at micro-/nano-scales.

Liquid superlubricity of lubricants containing hydroxyl groups and their aqueous solution under rolling/sliding conditions

Macroscale rolling/sliding conditions are in the superlubricity, a little-studied topic so far. The purpose of this paper is to examine the formation of elastohydrodynamic lubrication (EHL) films by water-based lubricants (glycerol and polyethylene glycol (PEG)), providing superlubricous friction. Experiments were carried out on an optical ball-on-disc tribometer under rolling/sliding conditions. The film thickness was measured by the thin film colorimetric interferometry, and the viscosity of liquids was measured by rotational and high-pressure falling body viscometers. The results show that tribochemical reactions are not the mandatory reason for friction to reach the superlubricity level when using the water-based lubricants. The studied liquids themselves are almost Newtonian. With the addition of water, the signs of shear thinning behavior disappear even more. Suitable conditions for this type of lubricant can be predicted using the known Hamrock–Dowson equations. An anomaly in the thickness of the lubricants was observed as an abrupt change at certain conditions. The more PEG there is in the lubricant, the higher the thickness at the beginning of the jump.

Response of elastic/viscoelastic layers on an elastic half-space in rolling contacts: Towards a new modeling approach for elastohydrodynamic lubrication

The 3D quasi-static contact problem of a rigid sphere rolling on an elastic half-space covered by a thin viscoelastic/elastic layer is studied as representative of soft layered contacts in engineering, physics, and biomedical applications, as well as for its potential merit to model Elasto-Hydrodynamically Lubricated (EHL) contacts in specific EHL film behavior suggested in earlier research. The viscoelastic layer behavior is modeled with a standard linear solid (SLS) model with a single relaxation time. Two approaches are used, the foundation (Winkler) reduced model assuming unidirectional stress–strain behavior normal to the surface only and the Papkovich–Neuber potential model which, based on the complete Navier–Cauchy equations, accounts for non-local support and bending effects. The models are validated against literature and compared. Whereas coated/layered contact problem studies mostly consider relatively thick coatings, and results focus on the pressure distribution and the contact area size, in this paper we consider layers with a thickness much smaller than the contact radius, i.e. of the order of a thickness of a conventional EHL film. The details of the layer deformation, pressure profiles and subsurface stresses are presented and interpreted in terms of the underlying physics, in particular the thin layer limit common also in thin fluid layers. It is shown that two dimensionless parameters, the ratio of the elastic modulus between the layer and the substrate and the ratio of the layer thickness to the corresponding Hertz contact width, dominate the systematic response for elastic layered contact problems. And four dimensionless parameters with two extras, the Deborah number based on the Hertz contact width and the ratio of the two elastic limits of the SLS viscoelastic material, are needed and analyzed for viscoelastic layered contacts. The results presented provide a good framework for the understanding and interpretation of the effects of viscoelastic layers on the deformation and pressure distribution of contact problems. Finally, the capability of actually modeling EHL film behavior via a viscoelastic layer suggested by van Emden et al. (2017) is discussed.

Thermal Elastohydrodynamic Lubrication Analysis for Rolling Cone Enveloping End Face Worm Drive

To explore the thermal elastohydrodynamic lubrication performance of rolling cone enveloping end face worm drive, the mathematical model of thermal elastohydrodynamic lubrication is established based on the meshing theory of rolling cone enveloping end face worm drive and elastohydrodynamic lubrication theory. With the help of the numerical analysis software MATLAB, the thermal elastohydrodynamic lubrication performance under smooth conditions is selectively analyzed by the multigrid method. Besides, the effects of throat coefficient, cone apex radius and half cone angle of the rolling cone on thermal elastohydrodynamic lubrication performance are analyzed at the meshing out of the transmission pair. The results show that the thermal elastohydrodynamic lubrication film thickness at meshing out of the worm gear is the smallest; the oil film thickness, oil film pressure and oil film temperature are reduced from meshing in to meshing out. The oil film temperature at the interlayer is the largest. The oil film temperature at the end face worm surface is the smallest. The small half-cone angle of the cone apex radius and larger throat coefficient and cone apex radius may achieve better thermal elastohydrodynamic lubrication performance of rolling cone enveloping end face worm drive.

Thermal Elastohydrodynamic Analysis of a Worm Gear

This study explores the elastohydrodynamic lubrication (EHL) between the contacting tooth flanks of a worm gear with nonconjugate meshing action. The contact is characterized by a slender-like elliptical shape and high sliding. The geometry and contact conditions for the considered worm gear were obtained using tooth contact analysis. Based on that, the complete area of the worm gear contact was analyzed using a validated numerical EHL model considering non-Newtonian, thermal, and transient effects. The geometrical and kinematic design factors that influence EHL film formation in worm gears were identified and discussed. The results show the specific characteristics of worm gear EHL contacts, such as the very slender contact in the tooth root flank area, which diminishes the effect of the entrainment speed on film thickness. EHL film formation could be supported by increasing conformity between the flanks to make the contact less slender. By comparing the film thickness results against analytically obtained ones, relatively large differences were observed except for one formula for minimum film thickness.

Prediction of film thickness in starved EHL point contacts using two-phase flow CFD model

In grease lubricated rolling contacts, the oil bleeding from the grease bulk forms an elastohydrodynamic lubricating (EHL) film. When the amount of bled oil at the contact inlet is insufficient, starvation occurs leading to a decrease in film thickness. Although most grease lubricated bearings operate under starvation, the correlation of starvation and film thickness is not fully understood. In this contribution, a two-phase flow CFD model is proposed. This model allows a calculation of the oil/air flow field in the vicinity of starved contacts and its effect on EHL film formation. For starvation conditions, the results show a decrease of film thickness at the center line in flow direction, while the contact sides can still remain fully supplied by replenishment.

Analysis on the effect of starved elastohydrodynamic lubrication on the adhesion behavior and fatigue index of wheel-rail contact

Friction modifiers (FMs) are widely used in wheel-rail applications. This paper presents a method to analyze the starved elastohydrodynamic lubrication (EHL) of the wheel-rail surface coated with FMs. Combined with rough surface simulation techniques, starved EHL analysis and film thickness analysis, the pressure distribution and adhesion coefficient under different film thickness states are obtained. The effect of film thickness of the FM supply layers and surface roughness on the adhesion coefficient is studied. The adhesion coefficient increases with the decrease in the effective FM film thickness and increase in the surface roughness. Based on the subsurface stress model, the subsurface stress distribution is studied. Then the influence of FMs on the fatigue of wheel and rail is analyzed on the basis of the shakedown map. Finally, the fatigue index of rail is explored in starved EHL state.

Characterization of elastohydrodynamic contact film thickness under high frequency force excitation using a 2D unwrapping-based image processing technique

The elastohydrodynamic lubrication (EHL) in a bearing contact is the typical regime between rolling elements and raceways. Simulations carried out by different researchers show a significant influence of harmonic load on the EHL film behavior. The current study aims to validate previous numerical findings using high-speed interferometry measurements to investigate the EHL behavior under force vibrations. A new image processing method is proposed based on the 2D unwrapping algorithm to extract film thickness in both circular and elliptical contacts. The experimental results confirm the previous numerical findings in the literature. Finally, it is shown that the frequency of excitation directly affects the amount and amplitude of the modulation behavior of the EHL film.

Fluid–Solid Interaction Modeling of Elastohydrodynamic Lubrication Point Contacts

Abstract Elastohydrodynamically lubricated point contact was investigated using a two-way partitioned fluid–solid interaction (FSI) model. ansys Mechanical finite element modeling software was used to compute elastic (and plastic) deformation of the solid bodies, while ansys fluent computational fluid dynamics software was used to model the fluid with the Navier–Stokes equations. The current model is not limited by Reynolds equation assumptions, allowing for the investigation of pressure, viscosity, and temperature variation across point contact elastohydrodynamic lubrication (EHL) films. Solid body material stress distribution and fluid behavior such as cavitation were also investigated. The details of model development are described. Validation of the model is presented across a range of loads and speeds for cases when the Reynolds equation is applicable. The results are in excellent agreement. Various slide-to-roll ratios were investigated considering a non-Newtonian fluid with thermal effects to characterize lubricant properties within the EHL film. Results demonstrate notable lubricant viscosity and temperature variations within the EHL film thickness both along and perpendicular to the rolling direction for cases with high slide-to-roll ratio. Cavitation was also considered, and cavitation bubble lengths were found to agree well with results found in open literature. Finally, the effects of material plasticity on solid body response were investigated. The FSI model developed in this research provides new insights on a classical EHL problem.

Predicting EHL film thickness parameters by machine learning approaches

Non-dimensional similarity groups and analytically solvable proximity equations can be used to estimate integral fluid film parameters of elastohydrodynamically lubricated (EHL) contacts. In this contribution, we demonstrate that machine learning (ML) and artificial intelligence (AI) approaches (support vector machines, Gaussian process regressions, and artificial neural networks) can predict relevant film parameters more efficiently and with higher accuracy and flexibility compared to sophisticated EHL simulations and analytically solvable proximity equations, respectively. For this purpose, we use data from EHL simulations based upon the full-system finite element (FE) solution and a Latin hypercube sampling. We verify that the original input data are required to train ML approaches to achieve coefficients of determination above 0.99. It is revealed that the architecture of artificial neural networks (neurons per layer and number of hidden layers) and activation functions influence the prediction accuracy. The impact of the number of training data is exemplified, and recommendations for a minimum database size are given. We ultimately demonstrate that artificial neural networks can predict the locally-resolved film thickness values over the contact domain 25-times faster than FE-based EHL simulations (R2 values above 0.999). We assume that this will boost the use of ML approaches to predict EHL parameters and traction losses in multibody system dynamics simulations.

The unresolved definition of the pressure-viscosity coefficient

In the classical approach to elastohydrodynamic lubrication (EHL) a single parameter, the pressure-viscosity coefficient, quantifies the isothermal pressure dependence of the viscosity for use in prediction of film thickness. Many definitions are in current use. Progress toward a successful definition of this property has been hampered by the refusal of those working in classical EHL to acknowledge the existence of accurate measurements of the piezoviscous effect that have existed for nearly a century. The Hamrock and Dowson pressure-viscosity coefficient at high temperature requires knowledge of the piezoviscous response at pressures which exceed the inlet pressure and may exceed the Hertz pressure. The definition of pressure-viscosity coefficient and the assumed equation of state must limit the use of the classical formulas, including Hamrock and Dowson, to liquids with high Newtonian limit and to low temperature. Given that this problem has existed for at least fifty years without resolution, it is reasonable to conclude that there is no definition of pressure-viscosity coefficient that will quantify the piezoviscous response for an analytical calculation of EHL film thickness at temperatures above ambient.

A multi-physics transient wear model for helical gear pairs

This study combines the use of a Tooth Contact Analysis (TCA) model for helical gear pair conjunctions with a multifaceted tribological model, implicitly coupled with a multi-body dynamic system. A reduced order 2-D Elastohydrodynamic Lubricant (EHL) film thickness prediction facilitates the estimation of viscous and boundary friction with a Greenwood-Tripp asperity model, as well as a lubricated wear methodology. An implicit approach is used to capture progressing wear upon gear teeth with consideration of gear microgeometry. The use of the numerical EHL model gives new insights to the coupled evolution of wear and dynamics on efficiency and NVH throughout the component’s life cycle.