Elastohydrodynamic Lubrication Film Thickness Research Articles

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 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.

Study on the flash temperature phenomenon in the contact area of rolling bearings

PurposeDue to high speeds, heavy loads, large slide-to-roll ratios (SRR) and other variable operating conditions, some rolling bearings that have been working in harsh conditions may experience flash temperatures in the contact area, which may result in early damage like smearing and then affect service life. This study aims to investigate the flash temperature phenomenon of rolling bearings through theoretical and experimental analysis.Design/methodology/approachA technology for measuring temperature distribution in rolling ball on disk contact under lubrication was developed. The test-rig can simulate the ball bearing contact. The effects of working conditions such as entrainment speed, load, SRR and lubricating oil viscosity on the flash temperature were investigated.FindingsThe results of the theoretical calculation and experiments indicate that the parameters promoting the reduction of film thickness in elastohydrodynamic lubrication are always related with the number of flash points, even film thickness reduced to mixed lubrication. The flash temperature is easier to happen in conditions of high SRR, heavy load, slow entrainment speed and low viscosity oil.Originality/valueThis work conducts an experimental study on the flash temperature phenomenon, providing a test technology for bearing lubrication and failure investigation.Peer reviewThis author has opted into Transparent Peer Review available at: https://publons.com/publon/10.1108/ILT-04-2023-0104

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.

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.

Quantifying the inlet pressure and shear stress of elastohydrodynamic lubrication

Central film thickness in elastohydrodynamic lubrication is governed by lubricant properties in the low-pressure contact inlet. A relevant definition of pressure-viscosity coefficient would require knowledge of the maximum inlet pressure. The maximum inlet shear stress determines if the Newtonian assumption is valid. Using numerical simulations, the maximum inlet pressure is found, wherein changes in viscosity continue to influence film thickness. It is found to depend on operating conditions, and it ranges from 50 to 185 MPa. The maximum inlet shear stress is found to reach up to 2 MPa. Analytical formulas are offered for predicting maximum inlet pressure and shear stress. These allow for a refined definition of the pressure-viscosity coefficient, restricted to a clearly-defined contact inlet.

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.

A discussion of Yu, M., Zhang, J., Joedicke, A., & Reddyhoff, T. (2021). Experimental investigation into the effects of diesel dilution on engine lubrication. Tribol. Int., 156, 106828

The recent rapid progress in the understanding and prediction of film thickness in elastohydrodynamic lubrication (EHL) has been the result of a shift in method from the classical treatment of viscosity as an adjustable parameter to measuring viscosity in viscometers. See for example, Hooke et al. (2021) [1]. For researchers outside of EHL the latter method would appear to be the obvious best approach. However, measuring shear-dependent viscosity in lubricating oils is fraught with great difficulty because there are other phenomena which appear to be constitutive behavior. For example, viscous heating appears in viscometers as the decrease in viscosity with increasing shear rate and in many viscometers this was accurately described by the sinh-law model. The lack of understanding of thermal feedback in viscometers resulted in much wasted effort in EHL friction.

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.

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.

Two-dimensional generalized non-Newtonian EHL lubrication: Shear rate-based solution versus shear stress-based solution

Lubricant behaves non-Newtonian at high shear stress and high shear rate. The non-Newtonian shear behavior of oil such as shear-thinning, viscoelasticity, and limiting shear stress could have influences on almost all characteristics of an elastohydrodynamic lubrication (EHL) contact, that is, the central film thickness, the coefficient of friction, and the temperature rise in the lubricating film. For example, for lubricants of large molecular weight or of polymer blended ones, there can be inlet shear-thinning, which would reduce the EHL film thickness. For the EHL traction in a rolling/sliding EHL contact, it cannot be reasonably predicted without the consideration of non-Newtonian rheology. In EHL numerical studies, the non-Newtonian properties and the constitutive equations are expressed by the concept of generalized viscosity [Formula: see text], which can be either a function of shear rate [Formula: see text] or a function of shear stress [Formula: see text]. In this way, a non-Newtonian lubrication problem could be solved as a generalized Newtonian problem based on solvers for a Newtonian EHL problem. According to the function of the generalized viscosity [Formula: see text], numerical solutions can be classified into shear rate-based ones and shear stress-based ones. In this work, these two kinds of numerical solutions are revisited. And their efficiency is compared for a two-dimensional (2D) non-Newtonian point contact EHL problem (here 2D means non-Newtonian flow in both the x and y directions). Results show that the shear rate-based numerical solution has a higher efficiency than the shear stress-based one. The shear rate-based 2D generalized Newtonian method is more suitable to analyze multiple EHL contacts in angular contact ball bearings and gears with complex 2D flow and/or transient EHL lubrication problems.

Professor Duncan Dowson, a source of inspiration

The current paper highlights the contribution of the Dowson and Higginson work to numerical line contact elastohydrodynamic lubrication film thickness prediction and the Hamrock and Dowson contribution to the film thickness prediction in elliptical contacts. This paper shows that, even by today’s standards, both the numerical pressure and film thickness results and the curve-fitted film thickness predictions are very accurate. As for the elliptical results, the authors show that the original predictions remain surprisingly accurate for moderately elliptical contact. For very long elliptical contacts, their prediction does not tend to a line contact asymptote. This paper then concludes that the predicted pressure spikes by Dowson, Higginson, and Hamrock are correct in shape and amplitude, at least near pure rolling conditions.

Functionalized phosphate ionic liquids as additives in PEG with excellent tribological properties for boundary/mixed/elastohydrodynamic lubrication

The 2,4,6-triamino-1,3,5-triazin-1-ium dibutyl phosphate (NP44) and 2,4,6-triamino-1,3,5-triazin-1-ium diisopentyl phosphate (NP88) were prepared as additives of PEG. In terms of temperature, slip-to-roll ratio and concentration, the effect of additives on tribological performance was explored. Excitingly, PEG with NP44 and NP88 presents outstanding lubricating property because of stable protective films formed in boundary/mixed lubrication. Furthermore, it was found that NP44 and NP88 can enhance film thickness in elastohydrodynamic lubrication when PEG was supplied with a limited quantity. It is attributed to the fact that adsorption of additives can reduce the surface energy to delay the oil depletion on the lubrication track.

Influence of load and speed on tribological performance of Cu nanofluids in EHL line contacts

Abstract Nowadays, wear is the leading cause of common machine failure and significant use of lubricants is required to reduce such failure. Lubricants over the years have evolved from animal fats to mineral oils and now nanofluids. Nanofluids are the blend of nanoparticles and base lubricating oil. Copper nanofluids are used as efficient nanolubricants for contacting surfaces because of their high thermal and electrical conductivity. In this paper, influences of applied load and rotational speed on tribological performance of copper nanofluids have been investigated. The effect of viscoelasticity in terms of contact pressure and film thickness in elastohydrodynamic lubrication (EHL) has been also investigated. Experimental tests were performed on multispecimen tribometer machine in pin on roller (line contact) arrangement, using EN31-EN31, EN31-GM, EN31-PB, EN31-Al alloy as tribopairs. Results indicate that both contact pressure and film thickness do not have any significant effect after incorporation of viscoelastic effect in EHL line contacts of copper nanofluids. Coefficient of friction (CoF) for all the tribopairs have been increased with the applied load, with rotational speed for EN31-GM, EN31- Al alloy. However, for EN31-EN31, EN31-PB CoF decreases. Wear has been also shown to be increase with the increase of applied load and rotational speed.

Tribo-dynamic analysis of high-speed roller bearings for electrified vehicle powertrains

Roller bearings are critical components in electrified powertrains. At high speeds, the critical role of the elastohydrodynamic lubrication (EHL) cannot be ignored, necessitating a tribo-dynamic analysis. This paper investigates the behaviour of roller bearings under operating conditions present in high-speed electrified powertrains. The bearing motion is obtained experimentally using a novel experimental rig. The bearing centre's orbital motion is acquired from the experiment and used as the boundary condition for tribological analysis. Results reveal that the EHL film thickness increases from 0.2 to 1.9 μm across a speed range of 0–15 000 rpm. A comparison with conventional dry contact analysis shows that roller load can be underestimated if the lubricant film is neglected in the roller-race contact deformation.

Numerical Analysis of Grease Film Thickness and Thickener Concentration in Elastohydrodynamic Lubrication of Point Contacts

This article presents a numerical analysis of elastohydrodynamic lubrication (EHL) with grease in point contacts to predict the grease film thickness at low speeds, which can increase with decreasing speed and exceed the base oil film thickness by orders of magnitude. The grease film thickness is obtained by solving the EHL problem, taking grease flow as a single-phase flow with a non-Newtonian viscosity. The continuity equation for thickener is derived, taking grease flow as a two-phase flow of base oil and thickener and the network structure of the thickener as both a porous medium and a non-Newtonian fluid. The flow rate of the thickener network is obtained as the grease flow rate subtracted by the Darcy flow rate of the base oil. The thickener concentration is obtained by solving the continuity equation for the thickener. Numerical results show that the increase in film thickness at low speeds is due to an increase in the equivalent viscosity in the inlet of the contact, which is due to a decrease in the shear rate and an increase in the thickener concentration. At low speeds, base oil is more easily squeezed out of the inlet of the contact than the thickener network, which leads to an increase in the thickener concentration, because the shear stress due to the Newtonian flow of base oil decreases with decreasing the shear rate, whereas the yield stress of the thickener network is independent of the shear rate. A reasonable agreement between the numerical and experimental results validates the present model.

Fault Diagnosis Method for Deep Groove Ball Bearings 6008, 6208 and 6408 Based on 'Hertz's Contact Theory' Using Engine Oil and Gear Box Oil

A bearing is the machine component which allows relative movement between the components of machines and equipment, along with transmitting the load. The most commonly used bearings are the Rolling Element Bearing. Rolling element Bearings generally fail suddenly before giving any indication. Many monitoring methods are in use to monitor the condition of bearings. The existing methods are either very costly or require major changes in the setup. The present work is based on a method, simple and inexpensive and capable for online condition monitoring of rolling element bearings. The methodology includes analytical determination of the Elastohydrodynamic lubricant film thickness based on “Hertz’s Contact theory”. The formula developed includes the Electrical Resistance between balls and races of the bearings and the Electrical Resistivity of the lubricants. The Electrical Resistivity is determined by using a simple Test Rig. Further the Electrical Resistance is also determined by using a simple Electrical Circuit along with measuring instruments on Rolling Element Bearing Test Rig at different loads and speeds. The Electrical Resistance is directly related to the lubricant film thickness present between the balls and races of the bearings, more the thickness, more will be Electrical Resistance. Related formulae of lubricant film thickness were developed for test bearing 6008, 6208, 6408 and test lubricants 20W40 (Engine oil), G 90 (Gearbox oil). Experiments were performed for speed range from 800 rpm to 1200 rpm (in steps of 100 rpm), and load range from 40 Kg to 120 Kg (in steps of 20 Kg), on Rolling Element Bearing Test Rig. Useful conclusions are drawn at the end of the experimental work based on the results.