Elastohydrodynamic Contacts Research Articles

Mixed Friction in Fully Lubricated Elastohydrodynamic Contacts—Theory or Reality

Mixed friction in liquid-lubricated tribosystems is characterized by the simultaneous presence of liquid and solid friction. Liquid friction results from the shearing of the lubricant, and solid friction from deformation and adhesion. Elastic hysteresis and plastic deformation of the solids cause energy losses during deformation and the separation of molecular bonds between the solids causes energy losses during adhesion. The classic conception of mixed friction presupposes direct contact between rough solids for solid friction to exist. However, if hysteresis losses are fully accepted as a cause for solid friction, every fully lubricated elastohydrodynamic contact would ultimately be a mixed friction contact since the elastic deformations of the solids also cause a loss of energy induced by hysteresis. Thus, the classic conception of mixed friction should be expanded since mixed friction can occur even when solids do not have any direct contact.

Thickener Behaviour in Rolling Elastohydrodynamic Lubrication Contacts

This paper focuses on the study of thickener behaviour in elastohydrodynamic contacts using fluorescence microscopy and optical interferometry. A standard Ball-on-disc configuration tribometer was used as well as a newly developed Ball-on-ring configuration tribometer mimicking the conditions in a 6314 deep groove ball bearing. Three types of custom-made greases were used with the same base oil and Coumarin 6 fluorescent dye on the thickener. These greases contained no additives and were of the lithium complex and alicyclic di-urea type. It was confirmed that the behaviour of the grease was directly influenced by both the structure and type of thickener, and the differences were successfully observed by fluorescence microscopy. The concentration of thickener was found to change due to the formation or breakdown of the deposited thickener layer on the track. At low speeds, the alicyclic di-urea forms a thickener layer on the track that is more pronounced than the lubricating film formed by the base oil alone. The thickener layer formation also occurs at higher speeds when fully flooded conditions are beneficial in building the layer. Experiments with a Ball-on-ring tribometer show that the natural replenishment of the real contact geometry is more effective than on a Ball-on-disc tribometer, but the formation of the thickener layer on the track is more limited than in a Ball-on-disc tribometer with artificial replenishment. At higher velocities, a smaller but stable layer is formed where the layer does not change much from a certain velocity.

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.

Mechanism investigation on gear vibration-cavitation caused by tooth-pair lubricated contact

Elastohydrodynamic contact of gears under the influence of vibration induces cavitation and jet impact. To predict the evolution of cavitation and the degree of cavitation erosion in the gear contact region, the multi-phase flow cavitation model and gear dynamic model are coupled for simulating the cavitation effect in the gear lubrication region and the jet stresses at the tooth boundary under different load torques and rotational speeds. Moreover, the proposed model is confirmed to be valid through comparing to experimental results. The cavitation and jet impact intensity increase and mainly distribute at the outlet of tooth contact under high speed. Load torque mainly affects the cavitation oscillation, but there exists an expectation value that makes both the amplitude and intensity of the cavitation fluctuation and erosion low.

Machine Learning for Film Thickness Prediction in Elastohydrodynamic Lubricated Elliptical Contacts

This study extends the use of Machine Learning (ML) approaches for lubricant film thickness predictions to the general case of elliptical elastohydrodynamic (EHD) contacts, by considering wide and narrow contacts over a wide range of ellipticity and operating conditions. Finite element (FEM) simulations are used to generate substantial training and testing datasets that are used within the proposed ML framework. The complete dataset entails 915 samples; split into an 823-sample training dataset and a 92-sample testing dataset, corresponding to 90% and 10% of the combined dataset samples, respectively. The proposed ML model consists of a pre-processing stage in which conventional EHD dimensionless groups are used to minimize the number of inputs into the model, reducing them to only three. The core of the model is based on Gaussian Process Regression (GPR), a powerful ML regression tool, well-suited for small-sized datasets, producing output central and minimum film thicknesses, also in dimensionless form. The last stage is a post-processing one, in which the output film thicknesses are retrieved in dimensional from. The results reveal the capabilities and potential of the proposed ML framework, producing quasi-instantaneous predictions that are far more accurate than conventional film thickness analytical formulae. In fact, the produced central and minimum film thickness predictions are on average within 0.3% and 1.0% of the FEM results, respectively.

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.

Forecast of the Temperature Variation of an Elastohydrodynamic Contact by the Simple Exponential Smoothing Model (SES)

Forecast of the Temperature Variation of an Elastohydrodynamic Contact by the Simple Exponential Smoothing Model (SES)

Novel In-Situ Observation of the Grease Constituents in Elastohydrodynamic Contacts by Fluorescence Microscopy

Grease is important lubricant for ball bearings as it is used much more often than oil. However, mechanism of the lubrication is not completely clear, especially concerning the role of the thickener in the lubricating process. It was shown that contribution of the thickener to film thickness build-up varies with operating conditions. Also, its influence on the resistive torque of the bearing was proved. However, all studies were in-direct showing its effects. This paper presents new in-situ fluorescence method of the grease constituents’ observation, where both, thickener, and base oil can be observed independently. Two different fluorescence dyes are used to distinguish grease constituents with the use of different microscope setup. Moreover, the new method was tested on two different test rigs. First is typical ball on disc test rig widely used for study of elastohydrodynamic lubrication. Second is ball on ring test rig which more closely represents radial ball bearing conditions. It was shown that thickener engagement is very different for each geometrical configuration.

In-situ measurement of the meniscus at the entry and exit of grease and oil lubricated rolling bearing contacts

The lubricant inlet meniscus in a rolling element bearing acts as a reservoir that feeds the elastohydrodynamic contact, resulting in a sufficiently thick film to avoid wear. A shortening and/or thinning of the inlet meniscus towards the contact centre is an indicator of bearing starvation and impaired lubricant performance. This work introduces an ultrasonic method to measure meniscus dimensions. Using in situ ultrasonic sensors on a full-scale cylindrical roller bearing test rig, we show that ultrasonic waves can cause oil films to resonate, and that the resonant frequency is directly related to the film thickness. Using a benchtop rig we validate the relationship between resonant frequency and film thickness. This allows for the measurement of meniscus thickness and length in situ during bearing operation. Menisci were measured at both the inlet and outlet of rolling bearing line contacts while lubricated with different viscosity oils and grease. All lubricants used showed they could be monitored using this approach. The implication of this paper is that it is possible to measure a critically important lubrication mechanism during operation without major component modifications.

Elastohydrodynamics of contact in adherent sheets

Adhesive contact between a thin elastic sheet and a substrate arises in a range of biological, physical and technological applications. By considering the dynamics of this process that naturally couples fluid flow, long-wavelength elastic deformations and microscopic adhesion, we analyse a sixth-order thin-film equation for the short-time dynamics of the onset of adhesion and the long-time dynamics of a steadily propagating adhesion front. Numerical solutions corroborate scaling laws and asymptotic analyses for the characteristic waiting time for adhesive contact and for the speed of the adhesion front. A similarity analysis of the governing partial differential equation further allows us to determine the shape of a fluid-filled blister ahead of the adhesion front. Finally, our analysis reveals a near-singular behaviour at the moving elastohydrodynamic contact line with an effective boundary condition that might be useful in other related problems.

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.

Atomistic simulation of martensite decay

Molecular dynamics simulations were used to study the phenomenon of martensite decay in gears by deforming a grinding mark subjected to contact stresses exerted by a rigid plate. The velocities imposed on the rigid plate and the interatomic potential chosen to represent the interactions between the rigid plate and the grinding mark allow for a realistic representation of an elastohydrodynamic contact with an average friction coefficient of 0.05 and all values below 0.1. Due to the initial plastic deformation the height of the grinding mark reduces significantly between two loading cycles, consequently, during the second loading cycle the deformation is predominantly elastic and dislocations only nucleate during the first loading cycle. The diffusion of carbon atoms from the grinding mark leads to the formation of plate-like regions depleted in carbon and precipitation of cementite, the products of martensite decay, as observed experimentally.

A prediction method for adhesive wear of herringbone gear

The centering error is a unique error in the manufacturing process of herringbone gear. The relationship between centering error and tooth wear and the influence of centering error on the service performance of herringbone gear are rarely reported. In this paper, a wear prediction method of herringbone gear with centering error is proposed by comprehensively considering the coupling relationship between tooth wear evolution and centering error. Based on the mixed elastohydrodynamic lubrication theory and Hertz contact theory, the calculation equation of asperity contact pressure of tooth surface after tooth wear is derived and the influence of centering error on load shared by both sides of herringbone gear is analyzed, then the coupling relationship between tooth wear depth and contact pressure is studied. The distribution of contact temperature, asperity contact pressure and wear depth on tooth surface is obtained, and the effect of centering error on them is discussed, then the effects of roughness, input torque and rotation speed on wear of herringbone gear with centering error is analyzed. The results show that the contact temperature, asperity contact pressure, sliding distance and tooth surface wear depth on the advanced contact side of herringbone gear is greater than those of the delayed contact side due to the influence of centering error. And the wear depth of both sides is not uniformly distributed along the tooth width direction and the maximum wear depth is located in the initial meshing area and decreases nonlinearly along the line of action. Besides, the greater the roughness and input torque, the greater the difference between the wear depth on both sides, and with the increase of rotation speed, the wear depth decreases. The results also show that the wear depth can change the centering error, which changed the contact characteristics and load shared by both sides of the herringbone gear. The wear depth and centering error have a significant impact on the meshing and contact performance of herringbone gears, and their influence cannot be ignored in the study of herringbone gears. The results of this paper can provide theoretical support for wear resistance design of herringbone gear.

Investigation on tool properties for the production of components with micro textured surfaces

Defined surface micrcotextures offer potential for the friction reduction in elastohydrodynamic contacts and can thus increase the energy efficiency of technical systems. The production of prostheses, where microtextured surfaces can provide anti-bacterial effects is another application area. To manufacture these components economically in large quantities, forming processes are to be aimed at. Since lightweight parts are crucial in most application areas, the forming of sheet metal is the subject of current research. A major aspect of the presented investigation is the behavior of tool materials for the production of such microtextured sheet metal parts. Applying microtextures of varying geometries to the tools is a key challenge. Limitations in the accuracy of electrical discharge machining processes for the fabrication of micro cylinders, prisms and cuboids are therefore analyzed on the high-speed steels 1.3343 and 1.3244. In addition, the tool surfaces are characterized regarding their friction properties with case hardening steel as a contact partner. In this paper, the tool friction is analyzed for the steel 1.7131 (16MnCr5) with an initial sheet thickness of t0 = 2.4 mm, which is often utilized for high-wear applications due to its high strength and toughness. In this context, the friction behavior of the wax-containing lubricant Beruforge 150 DL made for bulk forming processes is compared with zinc-free high-performance lubricants Raziol CLF 65-400 of varying viscosity.

Numerical Study of Transient Elastohydrodynamic Lubrication Subjected to Sinusoidal Dynamic Loads for Rough Contact Surfaces

Abstract The purpose of this paper is to study the behaviour of transient elastohydrodynamic contacts subjected to forced harmonic vibrations, including the effect of surface waviness for concentrated counterformal point contact under isothermal conditions. Profiles of pressure and film thickness are studied to reveal the combined effects of sinusoidal external load and surface roughness on the lubrication problem. The time-dependent Reynolds’ equation is solved using Newton–Raphson technique. The film thickness and pressure distribution are obtained at different snap shots of time by simultaneous solution of the Reynolds’ equation and film thickness equation including elastic deformation and surface waviness. It is concluded that the coupling effects of the transient sinusoidal external load and wavy surface would result in increase in modulations of the pressure and film thickness profile in comparison to the case where the smooth contact surfaces are subjected to sinusoidal external load.

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.

Validation of a coupled multibody and TEHL simulation by a piston/cylinder component test rig

A tribological highly stressed contact in the actuating system of axial piston machines is located between the control piston and the control chamber. This paper presents a new type of component test rig for measuring the frictional force and the gap heights between piston and cylinder. For this purpose, the original system is reduced to the actuator system, whereby the real kinematics and the loading forces are maintained. The axial movement of the control piston and the pressure in the control chamber can be configured individually. The measurement results of different parameter variations are compared with the results of the simulation. The simulation based on a coupled multibody and TEHL simulation with a transient, three-dimensional, thermal elastohydrodynamic contact calculation.

Nonlinear dynamic model of elastohydrodynamic lubricated line contact

Nonlinear dynamic model of elastohydrodynamic lubricated line contact

Non-Hertzian Elastohydrodynamic Contact Stress Calculation of High-Speed Ball Screws

In order to eliminate the calculation error of the Hertzian elastohydrodynamic contact stress due to the asymmetry of the contact region of the helix raceway, a non-Hertzian elastohydrodynamic contact stress calculation method based on the minimum excess principle was proposed. Firstly, the normal contact stresses of the screw raceway and the nut raceway were calculated by the Hertzian contact theory and the minimum excess principle, respectively. Subsequently, the Hertzian solution and the non-Hertzian solution of the elastohydrodynamic contact stress could be determined by the Reynolds equation under different helix angles and screw speeds. Finally, the friction torque test of the double-nut ball screws was designed and implemented on a self-designed bed for validation of the proposed method. The comparison showed that the experimental friction torque was the good agreement with the simulated friction torque, which verified the effectiveness and correctness of the non-Hertzian elastohydrodynamic contact stress calculation method. Under the large helix angle, the calculation accuracy of asperity contact stress for the non-Hertzian solution was more accurate than that of the Hertzian solution at the contact region of ball screws. Therefore, the non-Hertzian elastohydrodynamic contact stress considering the asymmetry of the raceway contact region could more accurately analyze the wear depth of the high-speed ball screws.

Rapid analysis of the effects of surface and sub-surface defects in elastohydrodynamic contacts

Surface and sub-surface defects alter the stress distribution in the material and tend to significantly reduce the life of elastohydrodnamic (EHL) contacts. Where the defects lie well below the surface their effect may be obtained by taking the EHL pressures from standard analyses and using these to determine the stress distribution. However, defects lying closer to the surface can produce significant local displacements and alter the EHL pressures. Analysis is difficult because these displacements change as the defect passes under the conjunction and calculation tends to be extremely time consuming. This paper presents an extension to the perturbation technique used for the rapid analysis of surface roughness. This extension enables solutions for both two and three dimensional defects to be obtained rapidly. The procedure is outlined and a number of examples given.