Elastohydrodynamic Lubrication Simulation Research Articles

A Simplified Non‐Hertzian Wheel‐Rail Adhesion Model Under Interfacial Contaminations Considering Surface Roughness

ABSTRACTThe accuracy and efficiency of the wheel‐rail adhesion model are important to the wheel‐rail rolling contact issues. The purpose of this study is to develop a simplified non‐Hertzian wheel‐rail adhesion model under interfacial contaminations to predict the wheel‐rail adhesion coefficient. Firstly, a non‐Hertzian full elasto‐hydrodynamic lubrication (EHL) model was developed and applied to determine the wheel‐rail contact pressure and film thickness under interfacial contaminations. Then, the empirical formula of central film thickness available to non‐Hertzian wheel‐rail normal contact relating to train speeds, axle loads and material parameters were proposed based on a large number of non‐Hertzian full EHL simulation for smooth surface under interfacial contaminations using linear regression. The empirical non‐Hertzian central film thickness formula and minimum film thickness formula for wheel‐rail contact obtained in this paper show certain differences from the formulas based on Hertzian contact. Using the proposed non‐Hertzian central film thickness formula, a simplified non‐Hertzian wheel‐rail contact adhesion model was developed, and the adhesion coefficient was obtained at different speeds and compared with the field test data. The numerical results showed good agreement with field test data.

High-pressure rheological properties of polyalphaolefin and ester oil blends and their impact on lubrication

Different base oils are often blended to optimize lubrication effectiveness. For blends of polyalphaolefins (PAOs) and ester oils, while their boundary lubrication performance is well-studied, studies on their rheological properties and elastohydrodynamic lubrication (EHL) are limited. This study investigates the viscosity and EHL properties of PAO 8 and pentaerythritol tetra(2-ethylhexanoate) (PEB 8) blends at various blending ratios, pressures, and temperatures. Results showed that under certain conditions, viscosities of the blends are lower than either base oil. This phenomenon was explained from a molecular perspective. The pressure–viscosity relationship was fitted using the Doolittle-Tait free-volume model. Additionally, studies of EHL performance and simulations of different oils correlate the pressure–viscosity to EHL characteristics. These findings provide insights for future lubricant formulation.

Extrapolation of Hydrodynamic Pressure in Lubricated Contacts: A Novel Multi-Case Physics-Informed Neural Network Framework

In many technical applications, understanding the behavior of tribological contacts is pivotal for enhancing efficiency and lifetime. Traditional experimental investigations into tribology are often both costly and time-consuming. A more profound insight can be achieved through elastohydrodynamic lubrication (EHL) simulation models, such as the ifas-DDS, which determines precise friction calculations in reciprocating pneumatic seals. Similar to other distributed parameter simulations, EHL simulations require a labor-intensive resolution process. Physics-informed neural networks (PINNs) offer an innovative method to expedite the computation of such complex simulations by incorporating the underlying physical equations into the neural network’s parameter optimization process. A hydrodynamic PINN framework has been developed and validated for a variant of the Reynolds equation. This paper elucidates the framework’s capacity to handle multi-case scenarios—utilizing one PINN for various simulations—and its ability to extrapolate solutions beyond a limited training domain. The outcomes demonstrate that PINNs can overcome the typical limitation of neural networks in extrapolating the solution space, showcasing a significant advancement in computational efficiency and model adaptability.

Elastohydrodynamic lubrication simulation analysis and experimental verification of different tandem reciprocating rod seal systems

Utilizing multiple seals in tandem is a prevalent technique employed to enhance the reliability of hydraulic sealing systems. In this paper, based on the elastohydrodynamic lubrication simulation of a single seal interface, a methodology for evaluating the performance of tandem reciprocating rod seal systems is established by manipulating the boundary conditions of the seals based on the principle of flow conservation. Through the simulation of two sealing systems, it is observed that inadequate lubricating oil occurs in the second sealing ring when the first sealing ring surpasses its sealing performance. Conversely, if the second sealing ring outperforms the first one, pressure will be generated between them. Additionally, a self-constructed experimental platform is utilized, and the results demonstrate simulation accuracy within an error margin of less than 15% when compared to the corresponding experimental measurements.

Modeling and Simulation of Elastohydrodynamic Lubrication in Spur Gears

An analysis using computational modeling by finite elements of the phenomenon of elastohydrodynamic lubrication (EHL) was carried out for a transmission system of pinion gear in a crankcase with partial filling lubrication. The analysis utilized tribological studies describing the contact behavior characteristics of solid surfaces with the lubrication film caused by dragging and splashing. Furthermore, the characteristics of the Reynolds-Hertz model for this type of phenomena are described, as well as the equations of elastic deformation and elastic displacements along with the geometry of the non-concordant bodies in contact. This was done by modeling the Lagrangian-Eulerian type for non-Newtonian fluid, implementing multiphysics coupling methods. The pressure profile of the lubricant films, the temperature reached by the lubricant, and the von Mises stress at the contact were obtained, showing a good approximation with the related results, indicating a range of 30 MPa to 900 MPa of pressure in the lubricant film and von Mises stress ranging from 30 MPa to 100 MPa in the contact area of the gear tooth.

The role of the glass transition for EHL minimum film thickness

When the glass transition is considered in an EHL traction analysis, shear-thinning is not sufficient to explain experiments because there is no liquid behavior to shear-thin and a limiting stress is required. The usual approach of ignoring the glass transition and the associated previtreous pressure dependence has concealed the role of vitrification in establishing the minimum film thickness in real contacts. For the first time, the glass transition is considered in an elastohydrodynamic lubrication simulation along with the glass compressibility. Vitrification and the previtreous pressure response are necessary to predict the minimum film thickness in a point contact. Future numerical simulations should include the glass transition, both for the film thickness and, of course, friction.

Convergence of (Soft) Elastohydrodynamic Lubrication Simulations of Textured Slider Bearings

We study the convergence of elastohydrodynamic lubrication (EHL) simulations of textured slider bearings. EHL simulations are computationally expensive because the equations that describe the lubricant film pressure and the deformation of the bearing surfaces are coupled and, thus, must be solved simultaneously. Additional simulation requirements, such as maintaining a specific bearing load-carrying capacity or lubricant film thickness, further increase the computational cost because they impose additional constraints or add equations that must converge simultaneously with those that describe the lubricant film pressure and bearing surface deformation. We methodically quantify the convergence of EHL simulations of textured slider bearings as a function of simulation parameters, including different convergence metrics and criteria, but also cavitation models, texture design parameters, and bearing operating parameters. We conclude that the interplay between discretization, the convergence metric, and the convergence criterion must be carefully considered to implement numerical simulations that converge to the correct physical solution. Our analysis also illustrates that a well-designed convergence study can minimize the computational cost.

Implementation of a Finite Element Deformation Model Within an Elasto-Hydrodynamic Lubrication Numerical Solver for a Ball in Socket Tribopair

In the framework of the elasto-hydrodynamic lubrication simulation algorithms of lubricated tribopairs, a key role is played by the chosen deformation model, since it affects the surfaces’ separation, which guarantees the existence of a thin lubricant film thickness, even when the tribo-system is subjected to high loads. The aim of this article is to merge a finite element deformation model based on linear tetrahedra, previously developed by the same authors, within the Reynolds equation solver in the elasto-hydrodynamic mode, with reference to a generic ball in socket lubricated tribo-system. The main novelty of this research is the implementation of the finite element deformation model, allowing the authors to relate the deformation vector to the pressure one through an influence matrix which takes into account the spherical motion of the ball with respect to the socket. The computer code for the problem–solution was developed in a MATLAB environment and simulated a planar motion condition in terms of eccentricity and angular velocity vectors, in order to calculate the meatus fluid pressure field, surfaces’ separation, shear stress, deformation, and wear depth. The integration over time of the output fields led to the time evolution of the load vector, friction torque vector, and wear volume. Moreover, the lubrication algorithm takes into account the fluid non-Newtonian behavior and the surfaces’ progressive geometrical modification over time due to cumulated wear. The obtained results reproduced the classical elasto-hydrodynamic shapes of the involved quantities, following the meatus minimum thickness predicted by the Hamrock–Dowson model; furthermore, it provided information about the mechanical behavior of the whole bodies belonging to the spherical joint thanks to the finite element deformation model.

Thermal elastohydrodynamic lubrication simulation model for the tooth guidance contact of a single tooth gearbox under mixed friction conditions

This article presents a simulation model for thermal elastohydrodynamic lubrication of the tooth guidance (piston/cylinder) contact of a single tooth gearbox. A finite-element analysis provides the boundary conditions for the thermal elastohydrodynamic lubrication simulation. The finite-element analysis under dry conditions allows calculating the macroscopic deformed contact surfaces for the elastohydrodynamic simulation model. The Hertzian deformation should be calculated in the presence of a lubricant and not with a dry finite-element analysis. A recently presented method, based on the finite-element submodeling technique, is extended to remove the Hertzian deformation of the macroscopic deformed lubrication gap from the dry finite-element analysis. A mixed friction with measured rough surfaces using the averaged flow model and mass conserving cavitation is implemented as well. An example shows how optimization of the gearbox by application of the simulation model is possible.

Elastohydrodynamic lubrication simulation of reciprocating rod seal with textured rod

An elastohydrodynamic lubrication simulation of a reciprocating rod seal with a textured rod was developed, which can used to design the most optimum texturing parameters for reciprocating rod. Based on the viscoelasticity of the rubber material, the transient dynamic equilibrium conditions of the reciprocating rod seal with a textured rod was established. By solving the one- and two-dimensional lubrication equations, the fluid film pressure for different textures was calculated. The asperities contact pressure was solved by microscopic contact analysis. The fluid–solid coupling iterative solution in the sealing zone was realized by the modified stiffness matrix method. By using the above model, the effect of different texture types and parameters on the sealing performance was analyzed.

Influences of Iteration Details on Flow Continuities of Numerical Solutions to Isothermal Elastohydrodynamic Lubrication With Micro-Cavitations

Abstract Studying elastohydrodynamic lubrication (EHL) of line contacts involving micro-cavitations, this paper examines various numerical solutions with a focus on their explicit flow continuities from inlet to exit. For the first time, influences of relaxation details, error controls, differential schemes, and mesh densities on flow continuity in EHL are revealed systemically. Furthermore, hybrid relaxation factors are introduced, the line relaxation is enabled with earlier boundary-condition enforcement, and a typical iteration process is updated with a three-in-one iteration control. Such a process is further integrated with two different starvation/cavitation treatments: one explicitly adjusts reformation locations, and the other uses a fractional film content parameter to adjust the Couette term originated by Bayada et al. The mass conservation results for problems with multiple micro-cavitations occurring inside the lubrication region are compared, and flow curves clearly demonstrate satisfactory continuities. These insights are beneficial for EHL simulations.

Wear law in mixed lubrication based on stress-promoted thermal activation

Although several empirical wear formulas have been proposed, theoretical approaches for predicting surface topography evolution during sliding wear are limited. In this study, we propose a novel wear-prediction method, wherein the energy-based Arrhenius equation is combined with a mixed elastohydrodynamic lubrication (EHL) model to predict the point-contact wear process in mixed lubrication. The surface flash temperature and contact pressure are considered in the wear model. Simulation results are compared with the experimental results to verify the theory. The surface topography evolutions are observed during the wear process. The influences of load and speed on wear are investigated. The simulation results based on the Arrhenius equation relationship shows good agreement with the results of experiments as well as the Archard wear formula. However, the Arrhenius equation is more accurate than the Archard wear theory in some aspects, such as under high-temperature conditions. The results indicate that combining the wear formulas with the mixed EHL simulation models is an effective method to study the wear behavior over time.

The Load Distribution with Modification and Misalignment and Thermal Elastohydrodynamic Lubrication Simulation of Helical Gears

A non-uniform model of the load per unit of length distribution of helical gear with modification and misalignment was proposed based on the meshing stiffness, transmission error, and load-balanced equation. The distribution of unit-lineload, transmission error (TE), and contact press of any point on the contact plane were calculated by the numerical method. The feature coordinate system was put forward to implement the helical preliminary design and strength rating.The thermal elastohydrodynamic lubrication (EHL) model of helical gear was established, and the pressure, film, and temperature fields were obtained from the thermal EHL model.The maximum contact temperature and minimum film thickness solved by thermal EHL were applied to check the scuffing load capacity. The highest flash temperature and thinnest film occur in the dedendum of the pinion. The thermal EHL method to evaluate the scuffing load capacity is effective.

EHL Analysis of Spiral Bevel Gear Pairs considering the Contact Point Migration due to Deformation under Load

The actual contact point of a spiral bevel gear pair deviates from the theoretical contact point due to the gear deformation caused by the load. However, changes in meshing characteristics due to the migration of contact points are often ignored in previous studies on the elastohydrodynamic lubrication (EHL) analysis of spiral bevel gears. The purpose of this article is to analyze the impact of contact point migration on the results of EHL analysis. Loaded tooth contact analysis (LTCA) based on the finite element method is applied to determine the loaded contact point of the meshing tooth pair. Then, the osculating paraboloids at this point are extracted from the gear tooth surface geometry. The geometric and kinematic parameters for EHL simulation are determined according to the differential geometry theory. Numerical solutions to the Newtonian isothermal EHL of a spiral bevel gear pair at the migrated and theoretical contact points are compared to quantify the error involved in neglecting the contact point adjustment. The results show that under heavy-loaded conditions, the actual contact point of the deformed gear pair at a given pinion (gear) roll angle is different from the theoretical contact point considerably, and so do the meshing parameters. EHL analysis of spiral bevel gears under significant load using theoretical meshing parameters will result in obvious errors, especially in the prediction of film thickness.

Non-linear model order reduction for elastohydrodynamic lubrication simulations of polymer seals

Abstract In the field of elastohydrodynamic lubrication (EHL) simulations, the importance of considering non-linearities in the structure increases constantly. In most cases, the finite element method is used to discretize the non-linear continuum equations. Apart from this, model order reduction techniques are used in EHL simulations to decrease the number of unknowns and the computational time. However, the reduction methods typically used are limited to linear problems. The aim of this paper is to introduce a model order reduction technique to EHL simulations, that captures non-linear behavior. As an example, a hyperelastic 2D axially symmetric seal is reduced and coupled to the Reynolds equation. The simulation is accelerated by a factor of 10 and beyond while the non-linear properties are preserved.

Efficient running-in of gears and improved prediction of the tooth flank load carrying capacity

PurposeThe purpose of this paper is to determine parameters for an efficient running-in of gears and an improved method for the prediction of the tooth flank load carrying capacity.Design/methodology/approachIn this contribution, a model for the calculation of the pitting life of involute spur gears is introduced, which is based on an extension of the life model according to Ioannides and Harris for rough surfaces. To achieve the most realistic thermal elastohydrodynamic lubrication simulation and stress calculation possible, measured real surfaces and elastic-plastic material properties of the area close to the surface are used. Special attention is paid to the compatibility of the fatigue life calculation for heterogeneous rough surfaces and their consistent consideration in the lifespan calculation.FindingsA non-destructive running-in for twin-disc pairings can be performed using suitable operating parameters, which subsequently can be transferred to tooth flank tests. Using the extended life model according to Ioannides and Harris, an enhanced prediction of the tooth flank load carrying capacity is possible.Originality/valueThe developed extended life model includes a new numerical approach for calculating the tooth flank load carrying capacity. It has the potential to reliably support and hence to accelerate the design process of gears.

Numerical simulation of elastohydrodynamic lubrication for an elliptical contact

An elastohydrodynamic problem on elliptical contact is formulated and numerically solved. The mathematical model is described by a system of integro-differential equations and inequalities with boundary conditions. The direction of the rolling velocity vector with respect to the axes of the ellipse has a marked influence on the distribution of pressure and the lubricating film thickness in the contact area. The elastohydrodynamic contact parameters are determined depending on the compression force applied thereto. These results are useful for analyzing processes occurring in lubricated concentrated contacts.

Rolling–sliding contact fatigue of surfaces with sinusoidal roughness

Surfaces of mechanical components under combined rolling and sliding motions may be subjected to accelerated contact fatigue failure due to increased number of microscopic stress cycles and pressure peak heights caused by rough-surface asperity contacts. Available rolling contact fatigue (RCF) theories were developed mainly for rolling element bearings, for which the effect of sliding is usually insignificant. In various types of gears, however, considerable sliding exist in the critical tooth contact area below the pitch line, where excessive wear and severe pitting failures originate. Ignorance of sliding is most likely the reason why the conventional RCF models often overestimate gear fatigue life. This paper studies the effect of sliding motion on the contact fatigue life of surfaces with sinusoidal roughness that mimicks the topography from certain manufacturing processes. A set of simple equations for stress cycle counting is derived. Mixed elastohydrodynamic lubrication simulations are executed with the considerations of normal loading and frictional shear. Relative fatigue life evaluations based on a subsurface stress analysis is conducted, taking into account the two sliding-induced mechanisms, which are the greatly increased number of stress cycles and the pressure peak heights due to surface interactions. Obtained results indicate that sliding leads to a significant reduction of contact fatigue life, and rough surface asperity contacts result in accelerated pitting failure that needs to be considered in life predictions for various mechanical components.

A mixed elastohydrodynamic lubrication model for simulation of chemical mechanical polishing with double-layer structure of polishing pad

Mixed elastohydrodynamic lubrication (EHL) model has been used to study slurry flow and contact pressure distribution in the chemical mechanical polishing (CMP) process. However, in various mixed EHL simulation frameworks, only a single-layer polishing pad is considered. Consequently, the double-layer polishing pad, which is widely used in semiconductor industry, cannot be designed and optimized from the tribology perspective with the assistance of theoretical simulation. In this paper, multi-layered elastic theory (MLET), which is frequently used to calculate flexible pavement response to truck loading, is introduced into the mixed EHL model. Pad deformation calculated by the MLET has a similar accuracy to that by the 3D finite element method, but its computational cost is much lower. It is very important for accurate and efficient simulation of the tribological behavior and material removal rate (MRR) in CMP. Based on the new simulation method, advantages of a different double-layer structure of polishing pad are discussed. It is found that the upper-hard lower-soft pad has better performance for improving the uniformity of MRR when the wafer surface is uneven, but the boundary exclusion region is bigger than single-layer pad and upper-soft lower-hard pad. The upper-soft lower-hard pad has advantage to reducing the edge exclusion, but the effect is not remarkable when the thickness of the upper layer is not extremely thinner than the lower layer.

Effects of the radial force on the static contact properties and sealing performance of a radial lip seal

The radial force is a critical factor to determine the sealing performance of radial lip seals. The effects of radial force produced by garter spring and interference on the static contact properties and sealing performance of a radial lip seal are investigated by numerical simulations and experiments. Finite-element analysis and mixed elastohydrodynamic lubrication simulation are used. Radial force, contact width, temperature in the sealing zone, the reverse pumping rate and friction torque are measured. A critical value of interference for a cost-effectively designed radial lip seal is found. Spring force is required to compensate the decrease of the radial force because of the interference and used as a possible way to obtain intelligent control of sealing performance. The quantitative results gotten in this study could provide guide for the seal design and improvement.