Elastohydrodynamic Film Thickness Research Articles

Enhancing practical modeling: A neural network approach for locally-resolved prediction of elastohydrodynamic line contacts

When modeling bearings in the context of entire transmissions or drivetrains, there are practical limits to the calculation resources available to calculate single bearings or even contacts. In settings such as these, curve-fitting methods have historically been deployed to estimate the elastohydrodynamic lubrication conditions. Machine learning methods have the potential to enable more sophisticated physical modeling in the context of larger computation environments, as the evaluation time of a trained model is typically negligible. We present a neural network that accurately evaluates the locally variable elastohydrodynamic film pressure and film thickness distributions and explore its application to (e.g.) cylindrical roller bearings. Employing a neural network for the EHL film thickness calculations rather than the curve-fitted, simplified methods that are today’s standard can enable a more physically precise modeling strategy at almost no additional computational cost.

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.

Time-dependent reliability-based design optimization of main shaft bearings in wind turbines involving mixed-integer variables

Main shaft bearings are essential transmission components in wind turbines. The failure of the main shaft bearings is inevitably accompanied by catastrophic consequences. In this regard, this paper presents a time-dependent reliability-based design optimization (TRBDO) approach for main shaft bearings involving mixed-integer variables. The maximization of fatigue life and the elastohydrodynamic film thickness under the load spectrum are selected as optimization objectives. The time-dependent reliability and geometric correlation are determined as nonlinear constraints. An efficient two-stage enrichment strategy is introduced to handle the time-dependent probabilistic constraint with mixed-integer design variables. A mixed-integer nonlinear optimization method is developed based on a meta-heuristic algorithm to solve the formulated TRBDO problem. Eventually, the effectiveness and robustness of the proposed approach are demonstrated by a real application in a 5 MW wind turbine.

Is Elastohydrodynamic Minimum Film Thickness Truly Governed by Inlet Rheology?

Is Elastohydrodynamic Minimum Film Thickness Truly Governed by Inlet Rheology?

Influence of water content on elastohydrodynamic friction and film thickness of water-containing polyalkylene glycols

Lubricants with a functional water portion have demonstrated a drastic reduction in friction under elastohydrodynamic lubrication conditions. With water-containing polyalkylene glycols, superlubricity with coefficients of friction <0.01 have been measured in model and gear contacts. In addition to the low friction, their calorimetric properties make them particularly interesting for application in electrified vehicles because the liquid can simultaneously serve as lubricant for the gearbox and coolant for the electric motors and the power electronics. In this study, the influence of water content between 8 wt% and 40 wt% of water-soluble polyalkylene glycols on friction and film thickness in elastohydrodynamically lubricated rolling-sliding contacts such as in gears and bearings is investigated. A polyalphaolefine oil is used as a reference. Friction has been measured on a ball-on-disk tribometer and film thickness on an optical tribometer. For a water content of 40 wt%, superlubricity with coefficients of friction down to 0.004 are found. The decrease in friction is up to 95% compared to the polyalphaolefine reference. The measured film thickness decreases with increasing water content. For a water content of 8 wt%, the film thickness is similar to that of the polyalphaolefine reference while at the same time friction is still reduced by 81%. Depending on the friction and film thickness requirements of a specific tribosystem, the water content of a water-containing polyalkylene glycol can be chosen accordingly.

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.

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

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

Electrical Field Strength in Rough Infinite Line Contact Elastohydrodynamic Conjunctions

Rolling element bearings are required to operate in a variety of use cases that determine voltage potentials will form between the rolling elements and races. When the electrical field strength causes the dielectric breakdown of the intermediary lubricant film electrical discharge can damage the bearing surfaces. To reduce the prevalence and severity of electrical discharge machining an improved understanding of the coupled electrical and mechanical behavior is necessary. This paper aims to improve understanding of the problem through a combined elastohydrodynamic and electrostatic numerical study of charged elastohydrodynamic conjunctions. The results show the effect of amplitude reduction means that for typical surface topographies found in EHL conjunctions the maximum field strength is adequately predicted by the elastohydrodynamic minimum film thickness and potential difference. The paper also indicates the width of the elevated electrical field strength region is dependent on EHL parameters which could have important implications on the magnitude of current density during dielectric breakdown.

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.

Multi-Objective Robust Optimization of Deep Groove Ball Bearings Considering Manufacturing Tolerances Based on Fatigue and Wear Considerations

Abstract In designing any machine element, we need to optimize the design to attain its maximum utilization. Herein, deep-groove ball bearings have been chosen for optimization. Optimization has been done in such a way that the design is robust so that manufacturing tolerances can be considered in the design. Robust design ensures that changes in design variables due to manufacturing tolerances have a minimum effect on the objective function, i.e., its performance. Robustness is achieved by maximizing the mean value of the objective function and minimizing its deviation. For rolling element bearings, its life is one of the most crucial considerations. The rolling bearing rating life depends on dynamic capacity, lubrication conditions, contamination, mounting, manufacturing accuracy, and material quality, and thus, the dynamic capacity and elasto-hydrodynamic minimum film thickness have been taken as objective functions for the current problem. Rolling element bearings have standard boundary dimensions, which include the outer diameter, inner diameter, and bearing width for the case of deep-groove ball bearings. So the performance can be improved by changing internal dimensions, which are the bearing pitch diameter, ball diameter, the inner and outer raceway groove curvature coefficients, and the number of rolling elements. These five internal geometrical parameters are taken as design variables; moreover, five design constraint factors are also included. Thirty-six constraint equations are considered, which are mainly based on geometry and strength considerations. In the present work, the objective functions are optimized individually (i.e., the single-objective optimization) and then simultaneously (i.e., the multi-objective optimization). Nondominated sorting genetic algorithm (NSGA-II) has been used as the optimization tool. Pareto-optimal fronts are obtained for one of the bearings. Of many points on the Pareto-front, only the knee solutions have been presented . This paper shows that geometrically feasible bearings can be designed by optimizing multiple-objective functions simultaneously and by also incorporating the variations in dimensions, which occur due to manufacturing tolerance.

A lubricated tribocorrosion model incorporating surface roughness

This study presents an improvement of an existing tribocorrosion model developed for passive CoCrMo alloys. This model is based on an empirical formalism established by Duncan Dowson in his pioneering works on the relation between wear and elasto-hydrodynamic lubrication. The improvement consists in introducing surface topography features allowing for a mechanistic relation between lubrication and wear. The effective normal force accounting for the plastic deformation of passive metals during lubricated tribocorrosion was described through the real contact area, which in turn was related to the worn surface topography (roughness) and the elasto-hydrodynamic film thickness. The modified model was applied to results from dedicated tribocorrosion experiments obtained by varying the lubricant viscosity and the contacting surface roughness. Good correlations were found between the mechanical and chemical wear rates and corresponding variables, which validated the model. Further development of the model should include boundary film effects, third bodies build-up and time dependent evolution of the worn surface.

Hydrodynamic action in slicing PV polysilicon with a novel fixed and free abrasive combined wire sawing

This paper presents a novel fixed and free abrasive combined wire sawing which uses the diamond wire with surface abrasive-groups interval distribution and combines with free SiC abrasives slurry to obtain sliced surface that can be textured by acid etching. During the sawing process, the ability that the free abrasives lapping the sawn surface has a positive correlation with the elasto-hydrodynamic (EHD) pressure, and the appropriate size of the free abrasives is related to the minimum film thickness of the cutting coolant. In this paper, the EHD action during the FFACWS is analyzed, and the film thickness equation and Reynolds equation of the sawing area are deduced. The influences of feed speed, wire speed, wire tensioning force, cutting coolant viscosity, core wire diameter, and surface structure parameters on EHD pressure and film thickness are analyzed, which provides theoretical reference for selection of the free abrasives diameter and analysis of their lapping effect on the slice surface. The research results show that the EHD pressure changes periodically in the direction of the wire axis in the entire sawing area. The change period is the same as a structural change period of the abrasive area (AA) and the bare wire area (BWA) on the wire surface. In one period, there are two EHD pressure peaks. The size range of free abrasives should be greater than the protruding height of the fixed abrasives on the diamond wire and less than the minimum film thickness in BWA, so that the free abrasives can be constrained in BWA to lap the slice surface.

Your EHD Rig May Not Be As Elastohydrodynamic As You Think

Abstract The concentrated contact formed between a steel ball and a glass disc—the optical elastohydrodynamic lubrication (EHD) rig—has been the primary instrument for experimental investigations of elastohydrodynamic film thickness. It has been a source for values of pressure-viscosity coefficient, a difficult-to-define property of liquids. However, comparisons with the pressure dependence of the viscosity obtained in viscometers show little agreement. There are multiple reasons for this failure including shear-thinning and compressibility of the oil. Another reason for the poor agreement is the subject of this short note. The optical EHD rig using glass as one surface will only be in the piezoviscous-elastic (EHD) regime when the pressure-viscosity coefficient is large. For low values, it would be operating in the isoviscous-elastic regime (soft EHD).

Experimental investigation into the effects of diesel dilution on engine lubrication

The dilution of lubricant due to contamination with diesel fuel is an increasingly prevalent, potentially important and poorly understood issue. This study addresses two fundamental questions: 1) How does the change in lubricant rheology due to diesel dilution affect engine lubrication? 2) How is the chemical performance of lubricant components (base oil and performance additives) impacted by diesel dilution under different lubrication regimes (boundary/full film, hydrodynamic/elastohydrodynamic). This is achieved by testing three lubricant samples: 1) neat fully formulated 0W-30 engine oil, 2) fully formulated 0W-30 oil diluted with diesel at a concentration of 15%, denoted “0W-30D”, and 3) neat, fully-formulated 0W-16, with the same base oil components and performance additives as the 0W-30, but blended to give a viscosity equal to that of the diluted an equivalent “0W-30D”. Tribometer tests, including 1) low pressure, low shear viscosity, 2) Ultra-high Shear Viscosity (USV), 3) elastohydrodynamic film thickness, 4) Stribeck friction and 5) boundary friction and wear, are then conducted. To further emulate engine lubrication conditions, Stribeck curve measurements are performed on the three lubricants using a journal bearing test rig, fitted with a connecting-rod and commercial diesel engine shells. Results suggest that diesel dilution only slightly affects chemical additive performance (with friction modifiers being more inhibited than anti-wear additives) but does reduce both viscosity and film thickness. However, care must be taken in using viscometrics to predict dilution behaviour because 1) the pressure viscosity coefficient is also affected by diesel dilution which has implications for elastohydrodynamically lubrication contacts, 2) shear thinning means that viscosity modifier additives effects lose their functions at high shear rates; whereas diesel contamination affects viscosity behaviour throughout the whole shear rate range.

The effect of outer ring elastodynamics on vibration and power loss of radial ball bearings

Ball bearings are an integral part of many machines and mechanisms and often determine their performance limits. Vibration, friction and power loss are some of the key measures of bearing performance. Therefore, there have been many predictive analyses of bearing performance with emphasis on various aspects. The current study presents a mathematical model, incorporating bearing dynamics, mechanics of rolling element-to-races contacts as well as the elastodynamics of the bearing outer ring as a focus of the study. It is shown that the bearing power loss in cage cycles increases by as much as 4% when the flexibility of the outer ring is taken into account as a thick elastic ring, based on Timoshenko beam theory as opposed to the usual assumption of a rigid ring in other studies. Geometric optimisation has shown that the lifetime power consumption can be reduced by 1.25%, which is a significant source of energy saving when considering the abundance of machines using rolling element bearings. The elastodynamics of bearing rings significantly affects the radial bearing clearance through increased roller loads and generated contact pressures. The flexible ring dynamics is shown to generate surface waviness through global elastic wave propagation, not hitherto taken into account in contact dynamics of rollers-to-raceways which are generally considered to be subjected to only localised Hertzian deflection. The elastodynamic behaviour reduces the elastohydrodynamic film thickness, affecting contact friction, wear, fatigue, vibration, noise and inefficiency.

Multi-objective optimization in geometric design of tapered roller bearings based on fatigue, wear and thermal considerations through genetic algorithms

To improve the fatigue, wear and thermal based failures of Tapered Roller Bearings (TRBs) a multi-objective optimization technique has been proposed. Objective functions considered are: the dynamic capacity (Cd) that is related to fatigue life, the elasto-hydrodynamic minimum film thickness (hmin) that is associated to the wear life, and the maximum bearing temperature (Tmax) that is related to the lubricant life. This paper presents a non-linear constrained optimization problem of three objectives with eleven design variables and twenty-eight constraints. The said objectives have been optimized individually (i.e., the single-objective optimization) and concurrently (i.e., the multi-objective optimization) through a multi-objective evolutionary procedure, titled as the Elitist Non-dominated Sorting Genetic Algorithm. A set of standard TRBs have been selected for the optimization. Pareto-optimal fronts (POFs) and Pareto-optimal surfaces (POSs) are obtained for one representative standard TRB. Out of many solutions on the POFs/POSs only the knee-point solution has been shown in a tabular form. Life comparison factors have been calculated based on both the optimized and standard TRBs, and results indicate that the optimized TRBs got enhanced lives than standard bearings. To get the graphical impression of optimized TRBs, a skeleton of radial dimensions of all seven optimized bearings based on various combinations of objectives has been shown for one of the representative standard TRB. In few cases the multi-objective optimization has better convergence as compared to single objective optimization due to its inherent diversity by the principle of dominance. The sensitivity investigation has also been conducted to observe the sensitivity of three objectives with design variables. From the sensitivity analysis data, tolerances have been provided for design variables. These tolerances could be used by the manufacturing industry while producing TRBs.

Optimal design of spherical roller bearings based on multiple tasking operating requirements

PurposeThe fatigue, thermal and wear-based bearing lives are the most important factors in the design of spherical roller bearings (SRBs). The main novelty of the present work is consideration of thermal effects as an additional objective function. The dynamic capacity (Cd), the elasto-hydrodynamic minimum film thickness (hmin) and the maximum bearing temperature (Tmax) are related directly with overall lives of the bearing, and these constitute the multiple tasking operating requirements for the design of bearings.Design/methodology/approachThese tasks depend upon various bearing design variables and associated constraints to help in formulating the realistic design optimization problem and in the present work these have been used to get optimal designs of SRBs in the form of Pareto-optimum fronts by using genetic algorithms.FindingsThe optimized lives show higher values as compared to the standard lives and better design choices as compared to that are available in the literature. The robustness of obtained designs are shown by conducting the sensitivity analysis of optimized operating requirements by perturbing optimum bearing variables.Research limitations/implicationsThe robustness of the design could be improved by optimizing tolerances of design variables based on desired variation in multiple tasking operating requirements.Practical implicationsFor the aerospace and space applications such critical design of bearings are required based on multiple tasking operating requirements. For example for higher temperature application in gearboxes, turbines and drilling equipment.Originality/valueIn critical applications, multiple tasking operating requirements are essential and often bearings put limit to the life of satellites and aircraft, and bearing design methodology proposed and implemented in the present paper addresses these issues, especially addition of thermal issue in bearing design.

Effect of arbitrary entrainment angle in elastohydrodynamic lubrication elliptical and circular contacts

Conventional elastohydrodynamic lubrication models assume parallel surface velocities such as in cam-follower and ball bearing systems. However, many important machine elements like hypoid gear and spiral bevel, the sliding and entrainment velocities are along different directions that could possibly influence the elastohydrodynamic lubrication performance characteristics significantly. For such complex conditions, the existing film thickness formulae and shear-thinning correction factors available in the literature are not suitable. Therefore, this paper investigates the effect of arbitrarily oriented surface velocity vectors on elastohydrodynamic lubrication characteristics considering realistic rheological models and experimentally established viscosity–pressure and compressibility laws. The Reynolds equation employed herein includes the surface velocity components along both the reference axes in the plane of contact. The elastohydrodynamic lubrication film thickness is found to deviate up to a maximum of 61% with respect to its conventional value. This deviation in film thickness behavior is shown to be a function of ellipticity and shear-thinning parameters.

The Influence of Slide\u2013Roll Ratio on the Extent of Micropitting Damage in Rolling\u2013Sliding Contacts Pertinent to Gear Applications

Micropitting is a type of surface damage that occurs in rolling–sliding contacts operating under thin oil film, mixed lubrication conditions, such as those formed between meshing gear teeth. Like the more widely studied pitting damage, micropitting is caused by the general mechanism of rolling contact fatigue but, in contrast to pitting, it manifests itself through the formation of micropits on the local, roughness asperity level. Despite the fact that micropitting is increasingly becoming a major mode of gear failure, the relevant mechanisms are poorly understood and there are currently no established design criteria to assess the risk of micropitting occurrence in gears or other applications. This paper provides new understanding of the tribological mechanisms that drive the occurrence of micropitting damage and serves to inform the ongoing discussions on suitable design criteria in relation to the influence of contact slide–roll ratio (SRR) on micropitting. A triple-disc rolling contact fatigue rig is used to experimentally study the influence of the magnitude and direction of SRR on the progression of micropitting damage in samples made of case-carburised gear steel. The test conditions are closely controlled to isolate the influence of the variable of interest. In particular, any variation in bulk heating at different SRRs is eliminated so that tests are conducted at the same film thickness for all SRRs. The results show that increasing the magnitude of SRR increases the level of micropitting damage and that negative SRRs (i.e. the component where damage is being accumulated is slower) produce more micropitting than the equivalent positive SRRs. Measurements of elastohydrodynamic film thickness show that in the absence of bulk heating, increasing SRR does not cause a reduction in EHL film thickness and therefore this cannot be the reason for the increased micropitting at higher SRRs. Instead, we show that the main mechanism by which increase in SRR promotes micropitting is by increasing the number of micro-contact stress cycles experienced by roughness asperities during their passage through the rolling–sliding contact. Therefore, the asperity stress history should form the basis of any potential design criterion against micropitting.

An Experimental Study on Film Thickness in a Rolling Bearing for Fresh and Mechanically Aged Lubricating Greases

The lubricating film formation of greases has been widely studied using single contact ball-on-disc configurations. However, other than for oil, the film formation with grease is governed by starvation, which in a full bearing is clearly different from that of the single contact. In this paper, film thickness measurements for various greases in a shielded deep groove ball bearing will be presented. The results were obtained using an in-house-made film thickness measurement rig based on the ‘electric capacitance method’. It will be shown that the film thickness may deviate from the theoretical elastohydrodynamic film thickness calculated from the base oil and that the film thickness is not constant in time. It will also be shown that the film thickness for longer times is not only determined by the classical properties such as oil viscosity and grease bleed but also by shear degradation of its microstructure.