Rolling Point Contact Research Articles

Effect of Oil Dispersion on Lubricating Film Thickness Generation under Oil Droplet Supply Conditions

Oil–air lubrication has proven to be very effective for high-speed bearings because the oil supply in the form of droplets can be precisely controlled. This work uses optical interferometry to study the mechanism of lubricating film formation in rolling point contact with oil droplet lubrication. The effect of a double oil drop pair, where two oil droplets are positioned in mirror images about the central axis of the lubricated track, is examined. The process by which pairs of oil droplets approach and lubricate a bearing contact is analysed. This study also covers the effect of multiple oil droplets supplied in a tailored or a random dispersion pattern. Additionally, the effects of oil viscosity, entrainment velocity, and droplet distribution on starvation are also investigated.

Evolution and flow maps of the oil layer in successive rolling point contact systems: Bearing as a case

It is of great relevance to maintain an adequate and continuous lubricant oil supply to each contact region in successive rolling point contact systems, such as rolling bearings, rolling guides, and ball screws. As a case study, we implemented laser-induced fluorescence observations of the dyed oil in a ball bearing. It is found that there exists an oil layer evolution as the rotating speed increases, especially when it reaches some critical levels. The oil layer will break up and migrate out of the rolling contact traces, while the oil distribution changes. In addition, a series of air–oil two-phase flow simulations based on computational fluid dynamics models and the volume-of-fluid method are run to reveal the forming mechanism. Flow maps are of construction with the flow patterns and the oil distribution. The critical points of the flow pattern transitions and the oil distribution changes are highly coincident with the contour lines of Ca. The force extraction shows that the pressure gradient force caused by Sommerfeld pressures has different directions at the outlet and inlet zones. They tend to attract the outlet meniscus into the low-pressure area while pushing the inlet meniscus out of the high-pressure area. As a result, the oil layer will leave and migrate out of the rolling contact traces. The capillary force will always work against the pressure gradient force. Their competition and equilibrium may determine the flow pattern transitions, the oil distribution changes, and their close relationships with Ca.

Patterns of interfacial flow around a lubricated rolling point contact region

It is of great importance to develop an in-depth understanding of interfacial flow around a lubricated rolling point contact region (RPCR). Consideration of the flow patterns around an RPCR will be important for the lubrication, cooling, and cleaning of machine parts, such as rolling bearings and gearboxes. In this study, an experiment using laser-induced fluorescence and a simulation using computational fluid dynamics of interfacial flow around an oil-lubricated ball-on-disk RPCR are presented. The results show good agreement with each other, and the flow patterns are clearly classified. The forming mechanisms are analyzed in terms of force competition caused by inertia, viscosity, pressure gradient, and air–oil surface tension. Quantitative criteria are proposed to evaluate the behaviors at the air–oil interface and the transition of flow patterns. Analyses have shown that the competition between these forces drives the motion of the air–oil interface, and the formation of flow patterns can be considered a self-adjusting process for the air–oil interface toward the equilibrium positions of the forces. High surface tension is beneficial for maintaining interface stability and can prevent the meniscus from rupturing at an outlet and concaving at an inlet. High capillary numbers may increase the risk for outlet meniscus rupture and the degree of concavity of the inlet meniscus.

A Combined Experimental and Atomistic Investigation of PTFE Double Transfer Film Formation and Lubrication in Rolling Point Contacts

Solid lubricants such as polytetrafluoroethylene (PTFE) are used in rolling-element bearings (REBs) when conventional lubrication (i.e. by fluids or greases) cannot be applied owing to extreme operating conditions (e.g. high temperatures or vacuum). Often a double transfer film mechanism is used with a cage acting as a lubricant reservoir resupplying the REB with solid lubricant by cage wear. An increase in service life of such bearings requires a better understanding of the transfer processes in the sliding and rolling contacts. Here, we investigate the effect of PTFE resupply on friction and lubricant film formation in a steel/steel and steel/glass rolling contact by tribometry and classical molecular dynamics (MD). A ball-on-disk tribometer is enhanced by a pin-on-disk sliding contact that transfers PTFE to the disk. The experiment allows simultaneous in situ measurement of friction and film thickness by white light interferometry in the rolling point contact. Increasing the pin load results in an increased PTFE film thickness in the rolling contact accompanied by a significant decrease in friction. To elucidate the observed film transfer and friction mechanism, sliding MD simulations with a newly developed density-functional-based, non-reactive force field for PTFE-lubricated iron oxide surfaces are performed. A strong adhesion of PTFE chains to iron oxide drives transfer film formation, whilst shear-induced chain alignment within PTFE results in reduced friction. The simulations reveal an anti-correlation between PTFE film thickness and friction coefficient—in agreement with the experiments. These investigations are a first step towards methods to control PTFE transfer film formation in REBs.Graphic

Shakedown analysis and its application in pavement and railway engineering

This paper has been prepared in memory of Professor Scott Sloan. It first presents a brief review of the development of shakedown analysis methods for pavement and railway engineering problems. In particular, it describes a new lower-bound method using the concept of critical residual stress fields and an upper-bound method using a nonlinear programming technique, which were developed by the authors, and then extended and applied to solve various shakedown problems in pavement and railway engineering. Moreover, this paper summarises and compares shakedown solutions for pavement and railway engineering problems, whilst highlighting the key factors that influence the shakedown limits. In addition, this paper proposes a simple, unified shakedown limit equation for pavements and railways under repeated moving surface loads. The equation includes three terms, which represent the resistances from cohesion, self-weight of the underlying soil, and self-weight of any superficial rigid layers, respectively, in a format analogous to Terzaghi’s bearing capacity equation. Numerical results indicate that the coefficient in the cohesion term Ncsd depends on the soil friction angle; while the coefficient in the self-weight term Nγsd is controlled by the soil friction angle and a dimensional factor γa/c. Values of Ncsd and Nγsd for a typical rolling point contact problem are also presented and interpreted, which explain the different contribution ratios from the soil self-weight to the shakedown limits of pavement and railway problems.

Investigation of lubricant supply in rolling point contacts under starved conditions using CFD simulations

High friction and wear in rolling bearings are prevented by a lubricating film, which separates the contacting surfaces. In rolling contacts with limited lubricant supply, the film thickness decreases at high rolling speeds, as more lubricant is displaced than replenished. This lubricant depletion is known as starvation and may induce mixed lubrication due to a low film thickness. When estimating the bearing lifetime, a fully flooded lubrication, i.e. an unlimited lubricant supply, is usually assumed. This leads to an overestimation of film thickness in operating ranges where starvation occurs. Thus, considering the onset of starvation is crucial to reduce the risk of premature bearing failures due to high friction and wear in the mixed lubrication regime. Therefore, this contribution presents a method, based on computational fluid dynamics (CFD) simulations, to calculate the onset of starvation in oil lubricated point contacts.

Numerical investigation of effects on replenishment in rolling point contacts using CFD simulations

A lubricating film prevents a rolling bearing from high friction and wear by separating the contacting surfaces. In grease lubricated contacts the bled oil induces a hydrodynamic film formation. At high rolling speeds, more bled oil is displaced than replenished, which leads to lubricant starvation. To predict the film formation under starvation, the lubricant supply by replenishment must be determined. However, the effects on oil replenishment are not fully clarified. In particular, the effects of oil wettability as well as the available bled oil amount on the replenishment are not sufficiently investigated. Therefore, in this contribution the oil flow around a rolling point contact is examined under limited oil volume and in dependence of oil wettability, using CFD simulations.

Origin of the tribofilm from MoS2 nanoparticle oil additives: Dependence of oil film thickness on particle aggregation in rolling point contact

The lubrication effectiveness of MoS2 nanoparticles as an oil additive remains unclear, restricting its application in industry to reduce friction. The goal of this work was to explore the lubrication mechanism of MoS2 nanoparticles as an oil additive. In this study, the oil film thickness behaviors of MoS2 nanoparticles in poly-alpha olefin (PAO4) base oil, PAO4 with 3 wt% dispersant (polyisobutyleneamine succinimide, PIBS), and 0W20 engine oil were investigated using an elastohydrodynamic lubrication (EHL) testing machine. Following the EHL tests, the flow patterns around the contact area and the tribofilm covering rate on contact area were studied using optical microscopy to understand the lubrication mechanism. The results indicate that both the dispersant and nanoparticle aggregation significantly affected the oil film thickness. The expected oil film thickness increase in the case of 0.1 wt% MoS2 in PAO4 base oil was obtained, with an increase from 30 to 60 nm over 15 min at a velocity of 50 mm/s. Flow pattern analysis revealed the formation of particle aggregation on the rolling path when lubricated with 0.1 wt% MoS2, which is associated with a tribofilm coverage rate of 41.5% on the contact area. However, an oil film thickness increase and particle aggregation were not observed during the tests with 0.1 wt% MoS2 blended with 3 wt% PIBS as the dispersant in PAO4 base oil, and for 0.75 wt% MoS2 in 0W20 engine oil. The results suggest that nanoparticles responsible for tribofilm formation originated from aggregates, but not the well-dispersed nanoparticles in point contact. This understanding should aid the advancement of novel lubricant additive design.

Impact of Water on EHL Film Thickness of Lubricating Greases in Rolling Point Contacts

This paper investigates the influence of water on the EHL film thickness of six commercial lubricating greases under fully flooded and starved conditions. Although grease can absorb large quantities of water, separation occurs due to pressure and shear, leading to free water. This does not have an impact on the film thickness under fully flooded conditions. However, water does have an effect on the film thickness under starved conditions where the differences are related to the change in oil bleed. In the presence of water, an increase in oil bleed was found for lithium, lithium complex and polyurea grease. These greases showed a reduction in the levels of starvation and, therefore, thicker films. Water contamination led to lower oil bleed for calcium sulfonate complex greases, which led to an increase in starvation, and therefore, thinner films compared to their uncontaminated counterparts.

Film Forming Behavior of Greases Under Starved and Fully Flooded EHL Conditions

ABSTRACTImproving knowledge on the film forming behavior of greases is essential to be able to develop efficient greases. This article examines how operating conditions (e.g., temperature, lubrication condition [fully flooded/starved]) and base oil viscosity influence the film forming properties of greases by comparing the behavior of two lithium-based greases and their respective base oils in rolling point contact. It is found that the onset and degree of starvation is controlled by speed (u) × viscosity (ν)/load (W) factor (uν/W) and temperature and that low uν/W values promote entrainment of thickener into contact. Thus, grease with low base oil viscosity shows significant thickener entrainment in the low speed region compared to the one with high base oil viscosity, which leads to the formation of thickener-rich viscous material during extended running with the low base oil viscosity grease. The results suggest that the shape of the film thickness versus speed curve is viscosity and uν/W range dependent. Furthermore, for the test conditions used in this study, grease-lubricated contacts appear to shift from the initial fully flooded condition to starved condition over a prolonged running of 2 h. The results from this study concur with those reported in the literature that fully flooded oil elastohydrodynamic lubrication (EHL) theory or film thickness cannot be directly applied or taken as a guideline in grease-lubricated contacts.

An experimental and modeling assessment of the HCFC-R123 refrigerant capabilities for lubricating rolling EHD circular contacts

This work aims at investigating the capabilities of the hydrochlorofluorocarbon (HCFC)-R123 refrigerant for lubricating rolling elastohydrodynamic circular contacts. The viscosity pressure and temperature dependence of this fluid, used in oil-free compressors, are first studied in its liquid phase. Complementary data like density variations are taken from the thermo-physics literature. Besides, film thickness measurements using a ball-on-disk tribometer equipped with an interferometry facility have been performed under pure rolling conditions. For the same operating conditions, film thickness is then predicted from a numerical elastohydrodynamic model in which the viscosity and density dependencies with pressure and temperature are described using physics-based relationships, allowing a quantitative approach. The results obtained from the full numerical model, from the analytical elastohydrodynamic film-thickness expressions, and from the experiments show an acceptable agreement. They clearly reveal that indeed refrigerants can build up a reasonable film thickness for lubricating elastohydrodynamic rolling point contacts.

Линеаризованные динамические уравнения для равновесия и поворота велосипеда: тестовая модель и обзор литературы

We present canonical linearized equations of motion for the Whipple bicycle model consisting of four rigid laterally symmetric ideally hinged parts: two wheels, a frame and a front assembly. The wheels are also axisymmetric and make ideal knife-edge rolling point contact with the ground level. The mass distribution and geometry are otherwise arbitrary. This conservative non-holonomic system has a seven-dimensional accessible configuration space and three velocity degrees of freedom parametrized by rates of frame lean, steer angle and rear wheel rotation. We construct the terms in the governing equations methodically for easy implementation. The equations are suitable for e.g. the study of bicycle self-stability. We derived these equations by hand in two ways and also checked them against two nonlinear dynamics simulations. In the century-old literature, several sets of equations fully agree with those here and several do not. Two benchmarks provide test cases for checking alternative formulations of the equations of motion or alternative numerical solutions. Further, the results here can also serve as a check for general purpose dynamic programs. For the benchmark bicycles, we accurately calculate the eigenvalues (the roots of the characteristic equation) and the speeds at which bicycle lean and steer are self-stable, confirming the century-old result that this conservative system can have asymptotic stability.

Effect of Coulomb friction on the deformation of an elastica constrained in a straight channel with clearance

Abstract In this paper we consider the effect of friction force on the contact behavior of an elastica constrained inside a straight channel with clearance. The elastica is fed in the channel through a space-fixed input clamp and protrude out of an elastically suspended output clamp. The two pads of the output clamp are assumed to be pre-compressed. Coulomb friction is assumed to be present on the lateral walls of the channel and in the output clamp. Focus is placed on the relative motion between the input and output ends of the beam. The beam may buckle when the input end is pushed in the channel and the output end is stuck due to friction resistance. Four types of contact patterns between the elastica and the constraining channel walls may occur when the beam buckles; they are rolling point contact, combined rolling and sliding point contact, rolling line contact, and sliding line contact. When the friction resistance at the output end is overcome, the beam will protrude out of the channel. When friction is present between the elastica and the lateral walls, hysteresis occurs when the input end undergoes a load–unload cycle. A small-deformation theory is also developed for the case when the spacing between the constraining walls is small. As expected, the accuracy of the small-deformation theory deteriorates as the spacing of the constraining walls increases.

Application of the local strain approach on a rolling point contact model

A newly developed cold forming process, the linear flow splitting process, allows the bifurcation of thin metal sheets by severe plastic deformation (SPD). This process produces flanges with an ultra-fine grained (UFG) microstructure, which is characterized by an increased hardness and lower surface roughness in comparison to the material in as-received state. The technology is researched within the Collaborative Research Centre 666 (CRC 666) “Integral Sheet Metal Design with Higher Order Bifurcations”. The increased hardness and reduced surface roughness of the flanges make this technology suitable for manufacturing linear guide rails. In order to achieve the required reliability and fatigue strength, the assessment of the performance of the linear flow-split profiles with gradient microstructure is of great importance. When considering rolling contact fatigue, the examination of the mechanical behavior of the side of the flange with higher hardness due to the UFG microstructure is required. In order to reduce time and costs, a numerical method to determine the rolling contact fatigue behavior would be useful minimizing the normally applied experimental effort. The present work aims to check the applicability of the local strain approach for the evaluation of the rolling contact fatigue behavior of linear flow split components by a Finite Element (FE) analysis. The Hertzian theory is only valid for homogeneous materials and cannot be directly applied to the flanges with gradient microstructure. Therefore an accurate modeling of the material in order to take into account the gradient in the mechanical properties is required. In this paper the characterization of the material behavior under axial cyclic loading will be presented. These results will be used for the Bergmann damage parameter to analyze the rolling contact fatigue behavior. Some parameters required for the application of the Bergmann approach are determined by a numerical simulation of the rolling contact. Results are compared to rolling contact fatigue tests performed on a recently developed test rig under the assumption of rolling without sliding and neglecting the effect of surface roughness and residual stresses.

Effect of friction on the planar elastica constrained inside a circular channel with clearance

In this paper we consider the effect of friction force on the contact behavior of an elastica inside a circular channel with clearance. The elastica is partially clamped at both the input and output ends of the channel. Coulomb friction is assumed to be present at the output end and on the constraining walls. Focused is placed on the relative motion between the input end and the output end of the elastica. Shooting method is adopted to solve for the quasi-static behavior of the elastica movement. Four types of contact patterns between the elastica and the constraining channel walls may occur when the input end moves in and out of the channel; they are rolling point contact, combined rolling and sliding point contact, rolling line contact, and sliding line contact. When the input end undergoes a sinusoidal motion, the output end either ceases to move at all, or follows exactly the input end motion. These two phases of output end motion occur subsequently, one immediately after the other. In general, the output end lags behind the input end. Experimental observations on the lagging phenomenon at the output end confirm the theoretical prediction.

An exploration of the elastohydrodynamic— hydrodynamic transition through film thickness measurements in rolling point contacts

The numerical solution of the elastohydrodynamic lubrication (EHL) problem is often presented in charts where dimensionless parameters and asymptotic relationships are used. Among them, the so-called isoviscous rigid asymptote is especially interesting because it defines the transition between elastohydrodynamic and hydrodynamic regimes, or between piezoviscous—elastic and isoviscous—rigid problems, respectively. In other respects, the combination of moderate contact pressures (i.e. moderate piezoviscosity, low normal load, and/or large radii of curvature) and high viscosity and speeds (i.e. high hydrodynamic effect) is quite often found in working mechanisms, for instance in most flange contacts in roller bearings. Surprisingly, only a few papers have analysed and discussed these operating conditions. Based on experimental results obtained in the range of the Moes parameters 15< L<50 and 2< M<160 for pure rolling circular point contacts, the aim of this work is first to show how film thickness distributions are affected when the piezoviscous elastic to isoviscous rigid transition is approached. In this context, the relative values taken by the central and minimum film thicknesses will be particularly studied. The second objective is to compare our results with those predicted by elastohydrodynamic and hydrodynamic solutions for non-conformal contacts found in the literature. Finally, the exploration of mild EHL is dealt with and a former publication in which electrohydrodynamic very thin films and highly loaded thick film regimes were studied is completed.

Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review

We present canonical linearized equations of motion for the Whipple bicycle model consisting of four rigid laterally symmetric ideally hinged parts: two wheels, a frame and a front assembly. The wheels are also axisymmetric and make ideal knife-edge rolling point contact with the ground level. The mass distribution and geometry are otherwise arbitrary. This conservative non-holonomic system has a seven-dimensional accessible configuration space and three velocity degrees of freedom parametrized by rates of frame lean, steer angle and rear wheel rotation. We construct the terms in the governing equations methodically for easy implementation. The equations are suitable for e.g. the study of bicycle self-stability. We derived these equations by hand in two ways and also checked them against two nonlinear dynamics simulations. In the century-old literature, several sets of equations fully agree with those here and several do not. Two benchmarks provide test cases for checking alternative formulations of the equations of motion or alternative numerical solutions. Further, the results here can also serve as a check for general purpose dynamic programs. For the benchmark bicycles, we accurately calculate the eigenvalues (the roots of the characteristic equation) and the speeds at which bicycle lean and steer are self-stable, confirming the century-old result that this conservative system can have asymptotic stability.

Experimental results and analytical film thickness predictions in EHD rolling point contacts

In this work, we consider several types of lubricants—including non-Newtonian fluids—that were studied in EHD pure rolling point contacts under various operating conditions, leading us to explore a wide range of dimensionless parameters. The experimental results are compared with predictions given by the usual analytical EHL relationships and by more recently developed models. This broad comparison conducted with particular emphasis on minimum film thickness ( h m) showed a fair agreement between experimental data and a few predictions including some obtained from extended models. Commonly used elastohydrodynamic lubrication (EHL) models did not systematically give accurate h m estimation, whereas minimum film thickness not only is a yield value but also serves as a key parameter in estimating lubrication regimes.

Discussion: “Modeling of Film Thickness and Traction in a Variable Ratio Traction Drive Rig,” (Sharif, K. J., Evans, H. P., Snidle, R. W., and Newall, J. P., 2004, ASME J. of Tribology, 126(1), pp. 92–104)

Ordinary shear-thinning affects EHL film thickness by reducing the central thickness from the theoretical Newtonian value 1 and ordinary shear-thinning affects traction in point contacts by shifting the logarithmic traction gradient to higher rates 2 in a manner indistinguishable from a reduction in pressure dependence of low shear viscosity at high pressure 2. The models selected by the authors for shear-thinning are not recognizable as ordinary shear-thinning. The authors’ Eq. (10) was Eyring’s sinh law model for thixotropy 3. Thixotropy should not be an issue here since the traction fluid is not known to contain wax and in any event the waxy structures studied by Eyring were quite weak with approximately τo=0.01 MPa3. Eyring made very clear his opinion that the sinh law, Eq. (10), is not an accurate description of shear-thinning 4. The authors’ Eq. (11) is not constitutive as it results from inhomogeneous shear 5. The viscosity extrapolation rule selected by the authors also has no physical basis. Two years ago, at the request of one of the authors for an accurate extrapolation, one of the discussers (S.B.) provided the authors with the parameters of the Tait-Doolittle free volume formulation for the same early version of Santotrac 50 6. This free volume formulation has been used by physical chemists to extrapolate viscosity to the glass transition pressure 7 in order to calculate pressure fragility. We have found it to be accurate for pressure extrapolations for another traction fluid 8. The authors neglected this formulation in favor of exponential extrapolation and thus discount the greater-than-exponential response that is known to be a feature of glass forming liquids and that the authors acknowledge to be important. Numerical simulations should ideally provide traction and film thickness predictions from the best available viscosity-temperature-pressure correlation, but these simulations should include shear-thinning. For example the fluid studied in this paper, Santotrac 50, is known to contain a high molecular weight additive. Then even a central film thickness calculation must include shear-thinning to accurately predict the film thickness. To illustrate, the film thickness of the subject traction fluid was measured in rolling point contact at INSA Lyon and the data points are plotted in Fig. 1. The Newtonian solution of Hamrock and Dowson 9 using rheological properties obtained at INSA from the same sample is plotted as a straight curve which can be see to overestimate the film thickness. The same film-thinning effect was reported by Makala et al. 10 for the same traction fluid. Shear-thinning of the ordinary power-law type is required to explain this film-thinning 11 that increases with sliding. The sinh law is inadequate for this purpose as the effect of sliding becomes drastic 11. Also, in Fig. 4 of the original paper, the viscosity of a glass is calculated with a free volume model that assumes a liquid equation of state. Free volume models are useful for their accuracy and for the fact that many of the parameters such as the glass transition temperature have physical meaning and may be obtained by other measurements.

The Linear Matching Method for Shakedown and Limit Analyses Applied to Rolling and Sliding Point Contact Problems

The Linear Matching Method for Shakedown and Limit Analyses Applied to Rolling and Sliding Point Contact Problems