Contact Elastohydrodynamic Lubrication Research Articles

Measurement of slip length and friction reduction: An experimental study about boundary slip using omniphobic and 2D coatings

There is an intrinsic link between boundary slip and superlubricity. However, due to limitations in experimental techniques, the slip length cannot be precisely measured, leaving the mechanism of boundary slip controversial. This paper aims to accurately measure the slip length at the solid-liquid interface under oil-lubricated elastohydrodynamic lubrication (EHL) conditions using experimental methods, and to explore the friction reduction due to boundary slip. The study reveals that both omniphobic (lotus leaf essence) coatings and two-dimensional (2D) material (MoS2) coatings facilitate boundary slip. The slip length measurement method proposed in this study builds a bridge between oil film thickness and slip length, successfully addressing a key issue in boundary slip research. The findings confirm the significant friction reduction due to boundary slip, representing a major advancement in reducing friction in oil-lubricated EHL contacts through boundary slip. Future research should focus on searching for coating materials with a slip length on the micrometer scale so that superlubricity could be achieved.

Truncation effects on circular EHL contact film thickness

Predictions of film thickness in elastohydrodynamic lubricated (EHL) contacts generally rely on the assumption of a semi-infinite equivalent solid to calculate elastic deformations. However, this assumption often fails when the contact is near an edge of one of the solids. This paper explores the impact of a solid edge being close to or within a theoretical EHL contact area on film thickness. We specifically highlight the advantages of a sharp edge over a chamfer, and the non-monotonous effect of the fillet radius on the minimum film thickness. Semi-analytical equations are developed to determine the maximum and minimum lubricant film thickness in a truncated contact and compare numerical results with experimental data in cases involving a chamfer.

Computational domain optimization for circular EHL contacts

This paper introduces an optimized computational domain for fully flooded circular elastohydrodynamic lubrication (EHL) contacts, enhancing the accuracy of numerical calculations of pressure and oil film thickness. First, the computational domain was configured based on Kapitza's analytical solution. Then, a resolution sensitivity study for the mesh of the 2D computational domain for the Reynolds equation was conducted to investigate the effect of mesh resolution on the accuracy of the numerical solution. Subsequently, the impact of the size of the full 3D computational domain on the simulation's accuracy and computational efficiency was analyzed. The main result is the 3D computational domain, which automatically adapts to operating conditions within the piezoviscous rigid, the isoviscous rigid, the piezoviscous elastic, and the isoviscous elastic regions, as well as in the transition regions between them. This results in a model which provides accurate predictions across a wide range of operational conditions. Another outcome is a new approximate expression for the central oil film thickness, showing a maximum relative difference of less than 4.6% compared to the numerical model.

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.

EFFECT OF ENTRAINMENT SLIDING DIRECTION TO THE TRACTION COEFFICIENT FOR EHL ELLIPTICAL CONTACTS IN THE LINEAR ISOTHERMAL REGION

Abstract In many mechanical systems, elastohydrodynamic lubrication (EHL) is apparent in the interfaces be-tween rolling/sliding parts. Even at small slide-to-roll ratios, detailed knowledge about the oil film thickness and the traction exerted by the highly pressurized lubricant is crucial for the efficiency and reliability of such systems. In this study, we explore the impact of surface velocity direction and contact ellipticity on traction characteristics within EHL through numerical simulations using an elliptical EHL contact solver based on a fully-coupled finite-element approach. We present a novel master curve that correlates the traction coefficient slope with the lubricant entrainment direction and ellipticity, for el-liptical EHL contacts in the piezo-viscous elastic (PE) regime. We demonstrate that the master curve, shows a maximum relative difference of less than 3.2% to the numerical simulation results, proving its efficacy. This curve is particularly beneficial for multibody dynamics models, providing a reliable tool for predicting frictional forces in systems where elliptical EHL contacts, operating within the PE regime at low SRR, are prevalent.

Effect of Indentation at Rolling Body Surfaces on the Film Formation in Elastohydrodynamic Lubrication Contact under Dynamic Loads

Vibration is one of the phenomena that can occur during the operation of roller bearing which can lead to dynamic loads being subjected to the contact and thus, affect the film formation in elastohydrodynamic (EHD) contacts. On the other hand, surface textures such as artificial indentations and grooves greatly affect the film formation as well as the corresponding pressure distribution in the contact area, since the depths of the textures are usually much greater than the film thickness in the contact. This paper investigates the influence of an artificial indentation located on the rolling element, which passes through a point contact under dynamic loads by means of numerical simulations. Solutions to the Reynolds equation are performed and calculations of the elastic deformation equation, force balance equation and lubricant properties equations to show the effects of both indentation passing through the contact and a sinusoidal dynamic load on the film thickness as well as pressure profile of EHD point contact. Moreover, the effect of frequency and amplitude excitation of the dynamic load on the film formation was investigated. The results revealed that the artificial indentation under sinusoidal dynamic load of EHD point contact induced a significant effect on the thickness of the film formation and pressure distribution.

A Novel Non-Contact Method for Monitoring the Acoustic Emission From Mixed Elastohydrodynamic Lubrication Contacts

Abstract Lubricated non-conformal contacts, such as between gear teeth, operate with high levels of mixed lubrication, where the amount of direct asperity contact depends on operating parameters that influence the film thickness. Understanding of the levels of surface interaction is key to optimizing component life, and there is considerable interest in sensitive monitoring methods such as Acoustic Emission (AE). Researchers have shown that AE can detect subtle changes in lubrication conditions, using sensors mounted directly on the rotating gears. However, the use of such sensors is complex and unsuitable for implementation in real gearboxes. The alternative, of using sensors placed on housings, is hampered by signal attenuation and noise. This paper presents a novel, non-contact stationary sensor, coupled by an oil film to the rotating gear, which is shown to be capable of detecting important changes in lubrication conditions with significantly higher consistency and precision than housing-mounted sensors, whilst avoiding the complexities of gear-mounted sensors.

A stiffness model for EHL contact on smooth/rough surfaces and its application in mesh stiffness calculation of the planetary gear set

A method for calculating time-varying mesh stiffness (TVMS) is proposed by developing a stiffness model for elastohydrodynamic lubrication (EHL) contact and integrating it into three-dimensional loaded tooth contact analysis (3D-LTCA). To enhance the accuracy and efficiency of the calculation, three projects have been implemented: Firstly, the contact deformation is modified, and the average slope is employed for calculating contact stiffness. Secondly, the lubricant film and EHL contact deformation are introduced into the deformation compatibility equations. Finally, the polynomial chaos expansion (PCE) surrogate model is employed to enhance computational efficiency. The proposed method is used to calculate TVMS of the planetary gear set, and the influence of speed, torque, and rough surface are analyzed. The results show that the previous method underestimating the TVMS of planet-ring gear pair in double-teeth meshing area under fluid lubrication, while the proposed method effectively addresses the issue. The different effects of the torque and speed on TVMS under mixed and fluid lubrication also have been revealed, emphasizing the significance of surface topography in gear meshing characteristics.

Transient mixed thermal elastohydrodynamic lubrication under startup and shut down conditions

The transient mixed lubrication behaviors in thermal elastohydrodynamic lubrication (TEHL) contacts during startup and stop are investigated. A transient mixed TEHL model for point contacts under time-varying speed conditions is proposed with comprehensive consideration of surface roughness, thermal effect, and transient behavior. The model is validated by the comparison to available published data. Based on the developed model, significant differences have been found compared with transient EHL and steady TEHL models. In addition, the transient mixed TEHL performance during start–stop with different acceleration rates and surface roughness is investigated. It shows that the lubrication behaviors during start–stop have an irreversible process. The roughness can significantly enhance the transient behavior. The roughness effect has a remarkable impact on lubrication performance in mixed lubrication. The evolution of lubrication behaviors during start–stop is highly related to the acceleration rate and surface topography.

A Fast Calculation Approach for Elastohydrodynamic Finite Line Contacts Applicable to Online Calculations of Rolling Bearing Models

Abstract Finite line contacts in rolling element bearings are usually under the regime of elastohydrodynamic lubrication (EHL). To obtain deeper insights into bearing performance, it is necessary to directly couple EHL contact models into bearing models. However, the existing EHL contact models are either too time consuming to be employed in the bearing model or too simplified to consider tilting contact behaviors and actual roller profiles. A fast calculation approach for EHL finite line contacts is proposed by combining the empirical film thickness formulas that have been developed for decades and an improved slicing technique that considers the coupling behaviors between slices. The proposed approach can not only predict the contact stiffness (normal contact stiffness and tilting contact stiffness) and contact states (contact pressure and film thickness) accurately but also is universal for different profiled contacts and material properties. The proposed approach costs only a few milliseconds for a single load case, which enables it to be directly employed in bearing models. Besides, the proposed approach is more of a framework, the use of which can be extended by involving different film thickness formulas and correction factors to consider complicated EHL behaviors such as thermal effects, shear thinning effects, surface roughness, lubricant starvation, and so on.

Dynamic characteristics investigation of a dual rotor-casing system considering the comprehensive stiffness of the intermediate bearing

This paper focuses on the vibrational properties of a dual rotor-casing coupled system with nonlinear clearance in the intermediate bearing, considering both the oil film stiffness and Hertzian contact stiffness between rolling elements and raceways. A comprehensive stiffness model for the intermediate bearing has been developed based on elastohydrodynamic lubrication (EHL) and Hertz contact theory. Subsequently, a dynamical model of the dual rotor-bearing-casing system is established using the finite element method, thereby verifying the feasibility of simulating the casing with beam elements. The dimensionality of the system equation is reduced using the fixed-interface component mode synthesis (CMS) method, and the resulting reduced-dimensionality equation is solved using the improved Newmark-β method. The effects of casing support, rotational speed, and radial clearance on the vibration characteristics of the system are investigated. Then, the comprehensive stiffness and coupled vibration characteristics of the system are analyzed to elucidate its intrinsic mechanism. Finally, the contact characteristics within the intermediate bearing under dynamic load are also studied. The results indicate that the support stiffness of the casing has a more significant impact on the second resonance caused by both the inner and outer rotors. The system is prone to experiencing varying compliance (VC) resonance at low rotational speeds. The excessive bearing clearance leads to complex vibrational characteristics of the system, making it challenging to predict its motion. The impact of minor changes in stiffness on system vibration is small when the comprehensive stiffness is large. At this time, the limited effect of oil film stiffness allows it to be disregarded in terms of comprehensive stiffness. Furthermore, the speed significantly influences the contact characteristics within the intermediate bearing under the unbalanced force of the rotor and gravity.

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.

Analysis on lubrication contact characteristics of imperfect transversely isotropic coating

Lubricated contact characteristics of transversely isotropic coating considering imperfect interface is of great importance in engineering to provide guidance on tribological design and optimization of tribo-pairs. The current investigation reports an elastohydrodynamic lubrication (EHL) contact model for transversely isotropic coating of imperfect interface. The interface is described by dislocation-like condition, i.e., displacement across it is transmitted discontinuously and such discontinuity is controlled by an imperfect index changing from 0 to 1. Based on this interfacial condition, frequency response functions (FRFs) of elastic field of imperfect transversely isotropic coating were derived, which was further used to establish the EHL contact model combined with the lubrication theory. The proposed model can be reduced to the one without coating, whose calculation results are consistent with those from literatures, providing a good verification. Finally, effects of imperfect index of interfacial displacement, coating thickness on film thickness, surface pressure, stress for transversely isotropic coating were investigated using the proposed model.

An original methodology to model stationary and transient starvation in EHL contact

Abstract Despite many researches in the past decades, starvation modelling of an ElastoHydrodynamic Lubricated (EHL) contact is still an arduous task. The well established Jackobson, Floberg and Olsson (JFO) theory indeed shows jumps discontinuities that are tricky to consider in a numerical solver. Two strategies are discussed in this paper. The first one uses a penalty method while the second one uses a moving mesh method. Their efficiency are compared to reference cases coming from the literature. Then, they are submitted to a transient analysis where the oil inlet layer decreases suddenly.

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.

A Simplified Thermal Plasto-Elastohydrodynamic Lubrication Model for Circular Contact With Real Surface Roughness

Abstract The current increase in power density, contact load, and speeds have imposed new challenges on elastohydrodynamic lubrication (EHL) contact models. To overcome possible EHL limitations under such conditions, the present work presents a unified thermal plasto-elastohydrodynamic lubrication (TPEHL) model for circular contact with real surface roughness capable to simulate the different lubrication regimes. Among the main characteristics of the proposed model, one should mention the minimal implementation changes in standard EHL models; there is no need for a preliminary assessment to verify whether thermal and plastic effects are negligible (or not) since these effects will naturally take place in the simulations, and good agreement between the predictions using the model and the experimental measurements.

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.

Experimental Analysis of Rolling Torque and Thermal Inlet Shear Heating in Tapered Roller Bearings

The investigation in this article focuses on the rolling resistance torque and thermal inlet shear factor in tapered roller bearings (TRBs) through systematic experiments using a modular test setup. TRBs typically operate under Elastohydrodynamic Lubrication (EHL) conditions. At sufficiently high speeds, the majority of rolling friction is due to a significant shift of the pressure centre in the EHL contact. While at lower speeds, sliding friction in the roller-rib contact becomes dominant, which operates under mixed lubrication conditions. Limited literature exists on the impact of inlet shear heating on effective lubricant temperature (Tin_c) and rolling friction in TRBs. To fill this gap, experimental measurements of the total frictional torque under axial loading at different speeds and oil temperatures are performed. With existing models for different friction contributions described in the literature, the rolling resistance due to EHL has been determined for various operating conditions. The effects of dimension-less speed (U), material (G), and load (W) parameters have also been investigated. Under fully flooded conditions, it was observed that the influence of material (G) and load (W) parameters on rolling friction is minor, while the impact of velocity (U) is significant. In the context of rolling resistance, the heating due to shear of the lubricant in the inlet zone plays a significant role. For higher rotational velocities, the estimated rotational torque reduction resulting from inlet shear heating was found to be approximately 6–8%.

Study the behaviour of transient elastohydrodynamic lubrication contact at motion start-up in the presence of surface roughness

PurposeThis study aims to present a numerical solution for the analysis of the influence of surface roughness as presented by a sinusoidal ripple of different amplitude and wavelength on the performance of transient elastohydrodynamic lubrication at motion start-up under different operational parameters of entraining speed and load as well as different acceleration rates.Design/methodology/approachA statistical asperity micro-contact model represented by a sinusoidal ripple expressed by two parameters (wavelength and undeformed amplitude) is considered. The ball equation of motion is used to calculate the force on the ball as it starts to move. The time-dependent Reynolds equation is solved together with surface deformation and statistical asperity models using the Newton–Raphson technique with the Gauss–Seidel iteration method.FindingsThe behaviour of the film thickness was found to be strongly influenced by the acceleration rate for different ripple amplitude and wavelength parameters. The effect of increasing the final entraining speed will eventually lead to rapid film thickness build-up and increase the film thickness jump at the moment of motion start-up. The effect of increasing applied load is to reduce the deviation of the minimum film thickness jump at the start-up of motion, making its value approximately equal to the steady-state value over the entire run-time period.Originality/valueInfluence of surface roughness for various wavelength and undeformed amplitude on the performance of transient elastohydrodynamic lubrication at motion start-up is presented at different acceleration rates as well as for different operating parameters of entraining speed and load. Ball equation of motion is used to calculate the force on the ball as it starts to move.

Characteristics in hard conformal EHL line contacts

PurposeInternal gearings are commonly used in transmissions due to their advantages like high-power density. To ensure high efficiency, load-carrying capacity and good noise behavior, a profound knowledge of the local gear mesh is essential. The tooth contact of internal gears relates to a convex and concave surface that form a conformal contact. This is in contrast to external gears, where two convex surfaces form a contraformal contact. This paper aims at a better understanding of conformal contacts under elastohydrodynamic lubrication (EHL) to improve the design of internal gearings.Design/methodology/approachAn existing numerical EHL model is used for studying the characteristic properties of a hard conformal EHL line contact. A hard contraformal EHL line contact is studied as reference. Non-Newtonian fluid behavior and thermal effects are considered. By taking into account the local contact conformity and kinematics, the effects and relevance of the curvature of the lubricant gap and micro-slip are analyzed. In a parameter study, scale effects of the contact radii on film thickness, temperature rise and friction are examined.FindingsThe curvature of the lubricant gap and effects of micro-slip are small in hard conformal EHL line contacts. For high micro-slip, it can be neglected. Hence, the modeling of conformal contacts using an equivalent geometry of the contact problem is reasonable. The parameter study shows beneficial tribological aspects of the conformal contact compared to the contraformal contact. Higher film thickness and lower fluid coefficient of friction are observed for conformal contacts, which can be attributed to lower pressures for the case of the same external normal force, or to a higher contact temperature rise for the case of equivalent contact pressure.Originality/valueDespite its widespread existence, the local geometry and kinematics in hard conformal EHL line contacts like in internal gearings have been rarely studied. The findings help for a better understanding of local contact characteristics and its relevance. The quantified scale effects help to improve the efficiency and load-carrying capacity of machine elements with hard conformal EHL contacts, like internal gearings.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-12-2022-0366/