Elastohydrodynamic Point Contact Research Articles

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.

An Investigation on the Teeth Crowning Effects on the Transient EHL Performance of Large-Scale Wind Turbine Spur Gears

Crowning is applied to wind turbine gears, including spur gears, to ensure adequate stress distribution and contact localization in wind turbine main gearbox gears to improve the gear performance in the presence of misalignments. Each gear tooth is crowned along the face width using a parabolic curve that graduates from a maximum height at the edges and vanishes at the center of the tooth flank. This crowning transfers the elastohydrodynamic contact problem from a line to a point contact case where the surface curvatures and pressure gradient are considered in both directions of the solution space. A wide range of longitudinal crowning heights is considered in this analysis under heavily loaded teeth for typical large-scale wind turbine gears. Furthermore, the variation in the velocities is considered in the analysis. The full transient elastohydrodynamic point contact solution considers the non-Newtonian oil behavior, where the numerical solution is based on the finite difference method. This work is focused on the evaluation of the effectiveness of teeth’s longitudinal crowning in terms of the consequences on the resulting pressure distribution and the corresponding film thickness. The modification of the tooth flank significantly elevates the film thickness levels over the zones close to the tooth edges without a significant increase in the pressure values. Moreover, the zone close to the tooth edges from both sides, where the pressure is expected to drop to the ambient pressure, is extended as a result of the flank modification.

Thermal-Elastohydrodynamic Contacts Lubricated With Oil/Refrigerant Solutions: A New Cavitation Modeling Approach Based on Refrigerant Solubility

Abstract A first cavitation modeling with thermal effects for oil/refrigerant solutions lubricated elastohydrodynamic point contacts is reported in this work. The solubility of the oil/refrigerant system is introduced into the generalized Reynolds equation coupled with the elasticity equation and the energy conservation equation. The numerical results show a very good agreement with the published experimental results concerning film thickness prediction. Moreover, the present model describes the cavitation region on a physical basis. A discussion with other cavitation models from the literature is proposed. It puts into light the necessity of taking into account the solubility of the refrigerant into oil for such problems. Compared to pure oil, oil/refrigerant solutions can potentially reduce the amount of liquid oil for the next contact due to its higher cavitation intensity.

Lubrication analysis and wear mechanism of heavily loaded herringbone gears with profile modifications in full film and mixed lubrication point contacts

The transient non-Newtonian thermal micro-elastohydrodynamic lubrication point contact model and the adhesive wear model in mixed lubrication point contact are applied to a heavy-loaded modified herringbone gear drive respectively in steady running phase and start-stop phase. The fundamental parameters of both elastohydrodynamic point contact and wear model are derived from the meshing characteristic and kinematics analysis of herringbone gears. The effects of pinion torque, rotational speed and surface roughness on the maximum pressure and temperature rise and the minimum film thickness are discussed in gear steady running condition for full film lubrication contact. Meantime, the asperity load ratio, contact flash temperature and tooth wear depth are investigated in gear start-stop phase for mixed lubrication point contact. The results show that the lubrication performance of herringbone gear is deteriorated by substantially increased pressure and temperature rise resulting from a larger tooth surface roughness and rotational speed. The tooth wear depth of herringbone gear in start-stop phase is likely greatly reduced with a larger start-stop acceleration. Moreover, the lubrication and wear performances for the complete running cycle of herringbone gear drive from start-up to stop indicate that large tooth surface roughness rather than high load are more prone to herringbone gear thermo-mechanical and wear failures.

Damping characteristics of thermal elastohydrodynamic lubricated point contacts

The present work envisaged the development of a novel method for computing the damping coefficients of thermal elastohydrodynamic lubricated point contacts based on energy conservation. The effects of load, entrainment velocity, and slide–roll ratio were studied, and the results were compared with the ISO thermal results. Multi-level method and discrete convolution fast Fourier transform method were employed to improve the solution convergence efficiency, and a sequential column sweeping technique was employed to solve the energy equations. The results indicated an increase in the damping coefficients with an increase in the load, and a corresponding decrease with an increase in the speed. When the entrainment velocity was relatively low, or the slide–roll ratio was relatively small, the influence of the slide–roll ratio was negligible. Subsequently, the relation between the damping coefficients and the load, speed, and slide–roll ratio was established using the least-square method.

Transient Analysis of Isothermal Elastohydrodynamic Point Contacts under Complex Kinematics of Combined Rolling, Spinning and Normal Approach

This paper presents a brief review of elastohydrodynamic analysis in commemoration of the immense contributions of Duncan Dowson. This paper also presents an elastohydrodynamic analysis of the elliptical point contact problem under steady state as well as transient conditions. The overall methodology is validated against numerical predictions and experimental observations of acknowledged historical sources. The validated methodology is used to make original contributions in the elastohydrodynamics of elliptical point contact subjected to complex combined contact kinematics, including rolling/sliding, mutual convergence and separation (squeeze film motion) of contacting pairs, when subjected to reciprocating and spinning motions. This combined complex contact kinematics under transient conditions has not hitherto been reported in the literature. This paper shows the critical role of squeeze film motion upon lubricant film thickness. The results also show that the influence of spin motion is only significant at fairly high values of angular velocity and in the absence of a rolling/sliding motion.

Effects of surface roughness on transient squeeze EHL motion of circular contacts with micropolar fluids

A numerical method was developed to study the effects of the micropolar (MP) lubricants at pure squeeze action in an isothermal elastohydrodynamic lubrication point contact with surface roughness under constant load condition, but without asperities contact. The modified transient stochastic Reynolds equation was derived in polar coordinates by means of the Christensen’s stochastic theory and the Eringen’s MP fluid theory. The Gauss–Seidel method and the finite difference method were both used to solve simultaneously the modified transient stochastic Reynolds, the load balance, the lubricant rheology and the elasticity deformation equations. The simulation results revealed that the effect of the MP lubricant was equivalent to enhancing the lubricant viscosity. Therefore, the central pressure and film thickness for MP lubricants were larger than those of Newtonian fluids under the same load in the elastic deformation stage. The maximum central pressure of the radial type roughness (RN) was greater than that of the circular type RN. The film thickness of the radial type RN was smaller than that of the circular type RN.

Numerical Solution of Elastohydrodynamic Lubrication for Sliding/Rolling Bearing for Non-newtonian Lubricant

There is always a demand in the industry sector to increase the efficiency of machine components to reduce wear and tear. This paper presents the numerical solution to the study of Elastohydrodynamic lubrication point contact for sliding/rolling bearing where the viscosity of the lubricant is non-Newtonian. The assumption that a lubricant is Newtonian reduces validation of the model hence the Reynolds-Eyring model in this research will incorporate the non-Newtonian nature of the lubricant of the bearing. The mathematical model comprises of Reynold-Eyring equation, film thickness, load balance, lubricant viscosity and lubricant density equations together with their boundary conditions. The Reynolds-Eyring equation governing the flow is non-linear hence the finite difference method numerical technique is used to discretize it together with the other two dimensional equations. These equations are solved simultaneously and Matlab software is used simulate the results. The film thickness and pressure profiles with various loads and speeds are presented. The findings note that an increase in load lowers the pressure and film thickness while an increase in the speed results to a direct increase in pressure and film thickness. A pressure spike is also noted at the exit of the bearing.

Investigation on stiffness and damping of transient non-Newtonian thermal elastohydrodynamic point contact for crowned herringbone gears

Abstract The stiffness and damping models of elastohydrodynamic point contact for herringbone gears with crown modification both in normal and tangential directions are developed. The lubrication performance of crowned herringbone gears in transient non-Newtonian thermal elastohydrodynamic point contacts are investigated to validate the developed models. The effects of operating and geometric parameters of crowned herringbone gear on stiffness and damping of elastohydrodynamic point contact are analyzed. The results show that in herringbone gear transmission, crown modification significantly affects oil film stiffness and damping. Low rotation speed substantially increases the damping. Helix angle contributes to the tangential stiffness and damping. This indicates that rationally selecting parameters can obtain appropriate oil film stiffness and damping to alleviate impact and vibration of herringbone gears.

Effect of laser surface texturing on friction behaviour in elastohydrodynamically lubricated point contacts under different sliding-rolling conditions

The Laser Surface Texturing (LST) technique has been largely investigated to improve the tribological performance of lubricated contacts. The present contribution is aimed at scrutinizing the influence of three texture configurations fabricated by LST on the tribological performance of elastohydrodynamic (EHD) point contacts under different slide-to-roll ratios (SRR), entrainment velocities and inlet temperatures. Friction experiments were conducted through a series of ball-on-disk tests in the MTM-2 (Mini-Traction Machine) tribometer. Main results showed that the texture configurations promoted significant effects under boundary and mixed lubrication conditions, and also affected the full-film EHD regime at higher temperatures. Furthermore, the tribological performance of textured samples was strongly related to the texture depth. Shallower texture designs (∼0.5 μm) reduced friction compared to untextured material, whereas deeper features (>1 μm) generally led to detrimental results. In general, dimples configuration decreased the lift-off speed and promoted full-film EHD conditions for a larger range of speeds, whereas radial curved grooves yielded to friction reduction under mixed lubrication conditions, moving the transition from boundary to mixed regimes to lower speeds, especially for intermediate lubricant viscosity.

Study on geometric contact model of elastohydrodynamic lubrication of arbitrary intersecting line gear

AbstractConsidering the tribology design theory of arbitrary intersecting line gear (AILG) is still a blank, the equivalent ellipsoid model of contact area of the AILG pair was built and then improved by 3 modification methods of line teeth profile. Based on the improved model, semiquantitative analyses of the relationship between the parameters of the AILG and the ratio of principal curvature radii of equivalent ellipsoid Rx/Ry were presented, and design criteria for the parameters of AILG based on elastohydrodynamic (EHL) point contact model were proposed. The results of the theoretical calculation and the optical EHL experiment proved that the modifications of teeth profile and the parameters design criteria for the AILG are conducive to improving its EHL performance.

Formulation of five degrees of freedom ball bearing model accounting for the nonlinear stiffness and damping of elastohydrodynamic point contacts

The knowledge of the dynamic behavior of rolling elements bearings and the contact properties have shown to be essential for model based fault diagnosis, lifetime estimation and reduction of noise in several industrial equipment application. This paper formulates the force and moments equilibrium of an angular contact ball bearing with five degrees of freedom accounting for the effects of the elastohydrodynamic (EHD) lubrication of its elements. A complete nonlinear model is derived and equivalent parameters for stiffness and damping of each contact were evaluated for different loading conditions. An iterative solution process was proposed to couple the bearing equilibrium and the EHD contact calculation, so as to generate the most suitable representation of the lubrication condition at the equilibrium point. The resulting reduced order model is promising to save computational costs and to make feasible the analysis of complex rotating systems supported by oil lubricated angular contact ball bearings.

A simplified approach for thermal elastohydrodynamic lubrication analysis of circular contacts using realistic lubricant properties

Thermal effect in elastohydrodynamic lubrication has been the subject of extensive research for several decades. The focus of this study was primarily on the development of an efficient numerical scheme to deal with the computational challenges involved in the solution of thermal elastohydrodynamic lubrication model; however, some important aspects related to the accurate description of lubricant properties such as viscosity, rheology, and thermal conductivity in elastohydrodynamic lubrication point contact analysis remain largely neglected. A few studies available in this regard are based upon highly complex mathematical models difficult to formulate and execute. The end-users may not have the specialized skill, knowledge, and time required for the development of computational codes pertaining to these models. Therefore, this paper offers a very simple approach to determine the distribution of mean fluid temperature within an elastohydrodynamic lubrication film. While it is an approximate method, it yields reasonably accurate results with only a little increase in computation time with respect to the isothermal case. Moreover, it can be added as a small module to any existing isothermal algorithm. Using this simplified thermal elastohydrodynamic lubrication model for point contacts, this work sheds some light on the importance of accurate characterization of the lubricant properties and demonstrates that the computed thermal elastohydrodynamic lubrication characteristics are highly sensitive to lubricant properties. It also emphasizes the use of appropriate mathematical models with experimentally determined parameters to account for the correct lubricant behavior.

On the crucial role of ellipticity on elastohydrodynamic film thickness and friction

The study reported here deals with elastohydrodynamic point contacts and it is focused on the influence of contact ellipticity. In five velocity–load reference cases, ellipticity was varied from slender to wide configurations, including the circular contact. For each case, Hertzian pressure, Hertzian area, load, and entrainment velocity were kept constant while the ellipticity was varied by changing the curvature radii. In this context, the maximum central film thickness did not occur for the infinitely wide contact, but for a slender configuration close to the circular case. Moreover, the minimum film thickness reached its optimum for a wide but finite elliptical contact. For low ellipticity ratios, specific film thickness features were obtained. In particular, very high central/minimum film thickness ratios are found. The cause of these behaviors was found in the change of the convergent shape. When the ellipticity was varied, the Poiseuille flows parallel and transverse to the entrainment direction were significantly modified and these modifications were quantitatively analyzed for the different cases. The competition between the Couette and the Poiseuille flows was totally different between the narrow and the wide elliptical contact, and this change was responsible for the film thickness variations with ellipticity. Ellipticity also had an effect on friction as it influenced the maximum pressure which in turn impacts the fluid viscosity.

Effects of out-of-contact lubricant channeling on friction and film thickness in starved elastohydrodynamic lubrication point contacts

This study presents experimental results on the effect of out-of-contact lubricant channeling on the tribological performance of nonconformal contacts under starved lubrication. Channeling of lubricant was carried out by adding a slider with a limited slot for scraping the displaced lubricant on one of mating surfaces (ball). Thus, the scraped lubricant is forced to flow back into the depleted track through the limited slot resulting in robust replenishment. The measurements have been conducted using optical tribometer (ball-on-disc) equipped with a digital camera and torque sensor. The effect of lubricant channeling was compared to the original contact condition by means of measuring friction and film thickness. The results show that the out-of-contact lubricant channeling leads to a significant enhancement of film thickness and friction reduction under starved conditions. Indeed, the starved elastohydrodynamic lubrication contacts transformed to the fully flooded regime after introducing the flow reconditioning. Moreover, the film thickness decay over time, which is common with starved elastohydrodynamic lubrication contacts, has not been observed in the case of lubricant channeling. However, the beneficial effect of lubricant channeling diminishes as the original contact condition tends to the fully flooded regime. The results of this study can be easily implemented in practical applications such as radial and thrust rolling-element bearings.

Numerical study on the interaction of transversely oriented ridges in thermal elastohydrodynamic lubrication point contacts using the Eyring shear-thinning model

Transient behaviour of tribo-characteristics caused by transversely oriented ridges on point contact surfaces was investigated based on a thermal elastohydrodynamic lubrication analysis. The ridges were assumed to exist on both the contact surfaces with different velocities. Results show that the interaction of ridges gives a large influence on the local film thickness, pressure, friction coefficient, temperatures on both the solid surfaces and temperature in the oil film. It is also pointed out that the size of the contact bodies brings strong effect on the temperature distribution and shear rate as well as on the friction coefficient. Furthermore, it is revealed that under rolling-sliding conditions, the shear-thinning property of the lubricant is negligible when the size of the contact body is large enough. However, shear-thinning effect plays an important role when the size is extremely small.

Particle Entrapment in Hybrid Lubricated Point Contacts

ABSTRACTThis study proposes an innovative approach for the study of particle entrapment in rolling element bearings (REBs). Two couples of contacting materials were considered, the classical steel–steel and silicon nitride–steel used in hybrid bearings. Numerical simulations, as well as experiments, combine theoretical trajectories for incoming contaminant particles and effective entrapment ratios observed within a twin-disc machine. Linking both approaches allows the highlighting of some key parameters leading to particle entrapment under pure rolling conditions in elastohydrodynamic point contacts.

Wavelet Based Numerical Solution of Elasto-hydrodynamic Lubrication Problems via Lifting Scheme

Wavelet theory is a relatively new and an emerging area in mathematical research, particularly wavelets are successfully used in fast algorithms for easy implementation. Elasto-hydrodynamic lubrication model involves coupled system as well as highly nonlinearity, is very difficult to solve numerically by standard methods to obtain better accuracy with low CPU time. The wavelet based schemes are appropriate to get a sufficient accuracy in low CPU time. In this paper, we present the wavelet based numerical solution of elastohydrodynamic lubrication line and point contact problems using lifting scheme. The proposed scheme gives higher accuracy in terms of super convergence in less CPU time, which has been illustrated through the test problems.

An approach for including the stiffness and damping of elastohydrodynamic point contacts in deep groove ball bearing equilibrium models

This work presents a methodology for including the Elastohydrodynamic (EHD) film effects to a lateral vibration model of a deep groove ball bearing by using a novel approximation for the EHD contacts by a set of equivalent nonlinear spring and viscous damper. The fitting of the equivalent contact model used the results of a transient multi-level finite difference EHD algorithm to adjust the dynamic parameters. The comparison between the approximated model and the finite difference simulated results showed a suitable representation of the stationary and dynamic contact behaviors. The linear damping hypothesis could be shown as a rough representation of the actual hysteretic behavior of the EHD contact. Nevertheless, the overall accuracy of the model was not impaired by the use of such approximation. Further on, the inclusion of the equivalent EHD contact model is equated for both the restoring and the dissipative components of the bearing׳s lateral dynamics. The derived model was used to investigate the effects of the rolling element bearing lubrication on the vibration response of a rotor׳s lumped parameter model. The fluid film stiffening effect, previously only observable by experimentation, could be quantified using the proposed model, as well as the portion of the bearing damping provided by the EHD fluid film. Results from a laboratory rotor–bearing test rig were used to indirectly validate the proposed contact approximation. A finite element model of the rotor accounting for the lubricated bearing formulation adequately portrayed the frequency content of the bearing orbits observed on the test rig.

Boundary Conditions for Elastohydrodynamics of Circular Point Contacts

The paper presents the solution of an elastohydrodynamic point contact condition using inlet and outlet lubricant entrainment with partial counter-flow. The inlet and outlet boundaries are determined using potential flow analysis for the pure rolling of contiguous surfaces. This shows that Swift–Stieber boundary conditions best conform to the observed partial counter-flow at the inlet conjunction, satisfying the compatibility condition. For the outlet region, the same is true when Prandtl–Hopkins boundary conditions are employed. Using these boundary conditions, the predictions conform closely to the measured pressure distribution using a deposited pressure-sensitive micro-transducer in a ball-to-flat race contact. Furthermore, the predicted conjunctional shape closely conforms to the often observed characteristic keyhole conjunction through optical interferometry. The combined numerical–experimental analysis with realistic boundary conditions described here has not hitherto been reported in the literature.