Elastohydrodynamic Lubrication Problem Research Articles

Study on the mixed lubrication of rough planar extrusion considering surface texture

Surface texture plays a crucial role in fluid dynamic lubrication. The non-Newtonian thermal elastohydrodynamic lubrication problem involving rough surfaces with texture has not been investigated to date. In this paper, a model for non-Newtonian thermal elastohydrodynamic lubrication incorporating rough surfaces and texture morphology is developed, focusing on the problem of mixed lubrication in planar extrusion with texture. The model builds upon the Reynolds equation with flow factor introduced. It considers the effects of rough surface texture, thermal effects, and non-Newtonian effects. The Reynolds equation is numerically solved using the Semi-System method to calculate the oil film pressure in full film region and contact pressure in dry contact area. The DC-FFT algorithm is employed to calculate surface elastic deformation. Comparing the calculated friction coefficient of the present model with the measured values in literature experiments, the average error is only 6.94%. Furthermore, the study investigates the effects of texture, temperature, and non-Newtonian on interfacial lubrication performance under mixed lubrication conditions. It’s found that compared to untextured surface, the average film thickness of textured surface increased by a maximum of 10.8%, and the friction coefficient decreased by a maximum of 67.4%; Compared to Newtonian fluids, shear thinning fluids reduce temperature by 0.18%, and shear thickening fluids are more conducive to improving mixed lubrication performance. A stepped pit texture is designed based on the dynamic pressure mechanism of the texture, indicating that the circular stepped pit texture has the best load-bearing capacity improvement.

Quantitative Elastohydrodynamic Lubrication—Seventeen Years In

Abstract Seventeen years have passed since the first full elastohydrodynamic lubrication (EHL) simulation employed the real pressure and shear dependence of viscosity measured in viscometers to accurately predict film thickness and friction. This is the appropriate time to enumerate the advances in understanding brought on by the application of high-pressure rheology to the EHL problem. The pressure dependence of the low-shear viscosity, which has been measured in viscometers for nearly a century, differs from the narratives taught to tribology students and often used to justify inaccurate models. The central film thickness often depends on the shear-thinning at low pressure and time–temperature–pressure superposition demands that the same shear dependence be active at the high pressure where friction is generated. In this article, some of the revelations resulting from quantitative EHL are reviewed. For example, it has been discovered that the minimum film thickness in point contacts depends upon the viscosity at the highest pressures of the contact. This explains the errors in the classical formulas, which were based upon the fictional narratives concerning piezoviscous response, and the assumption of film thickness governed by inlet conditions. Quantitative EHL provides quantitative predictions of contact behavior.

Performance of textured dual mobility total hip prosthesis with a concave dimple during Muslim prayer movements

The single mobility bearing as a previous bearing design of total hip prosthesis has severe mobility constraints that can result in dislocation during Muslim (people who follow the Islam as religion) prayer movements, specifically shalat that requires intense movement. There are five intense movements (i.e., bowing, prostration, sitting, transition from standing to prostration, and final sitting) during Muslim prayer that may generate an impingement problem for patients with total hip prosthesis. In this work, textured dual mobility total hip prosthesis with two textured cases (i.e., textured femoral head and textured inner liner) are presented and their performances are numerically evaluated against untextured surface model during Muslim prayer movement. The concave dimple design is chosen for surface texturing, while for simulating femoral head materials, SS 316L and CoCrMo is choosen. To represent the real condition, three-dimensional computational fluid dynamics (CFD) coupled with two-way fluid–structure interaction (FSI) methods are employed to analyze elastohydrodynamic lubrication problem with non-Newtonian synovial fluid model. The main aim of the present study is to investigate the tribological performance on dual mobility total hip prosthesis with applied textured surface with concave dimple in femoral head and inner liner surface under Muslim prayer movements. It is found that applying surface texturing has a beneficial effect on the lubrication performance for some intense movements. The textured femoral head model performs better than textured inner liner model and untextured model (both femoral head and inner liner). The numerical results also indicate superior performance of CoCrMo femoral head compared to SS 316L femoral head. These findings can be used as a reference for biomedical engineers and orthopedic surgeons in designing and choosing suitable total hip prosthesis for Muslims makes they can carry out Muslim prayer movements like humans in general who have normal hip joints.

Advanced modelling of lubricated interfaces in general curvilinear grids

Tackling fluid-flow problems involving intricate surface geometries has been the catalyst for a plethora of numerical investigations aimed at accommodating curved complex boundaries. An example is the application of body-fitted curvilinear coordinate transformation, where the one-to-one correspondence of grid points from a non-orthogonal curvilinear grid in the physical domain to an orthogonal grid in the computational domain is achieved. In lubricated interfaces, such conversion is challenging due to the complexity of the governing equations in the mapped-grid, the numerical instabilities exhibited by their non-linearities and the severity of the operating conditions. The present contribution proposes a Reynolds-based, finite volume fluid–structure interaction (FSI) framework for solving thermal elastohydrodynamic lubrication (TEHL) problems mapped onto orthogonal grids in the computational domain. We demonstrate how the strong conservation form of the pertinent governing equations can be expressed in three-dimensional curvilinear grids and discretised using the finite volume method to ensure fluid-flow conservation and enforce mass-conserving cavitation conditions. Numerical and experimental benchmarks showcase the robustness and versatility of the proposed framework to simulate a diverse range of lubrication problems, hence achieving a predictive computational tool that would enable a shift towards tribology-aware design.

Non‐spherical shape optimization of artificial hip joint based on elastohydrodynamic lubrication analysis

AbstractStructural optimization design is a promising way to further promote the lubrication performance of the artificial hip joint (AHJ). In this work, a non‐spherical shape optimization design strategy for the femoral head is firstly proposed. The generatrix, the line rotated about an axis that generates the bearing surface of the femoral head, is characterized based on a third‐order Bezier curve. The performance of the AHJ under steady‐state condition is analyzed by solving the governing equations of the elastohydrodynamic lubrication problem, and the minimum lubricating film thickness of the AHJ is maximized by adjusting the positions of four control points of the Bezier curve based on the simulated annealing method. The results show that, when compared with the standard spherical femoral head, the optimized non‐spherical femoral head can significantly improve the minimum thickness and reduce the maximum pressure of the lubricating film of the AHJ. Through the analysis of the optimization process, the results further reveal that the shape of the femoral head has a direct impact on the thickness distribution of the lubricating film. This research will provide guidance and theoretical support for novel design of AHJs.

Exact Model Order Reduction for the Full-System Finite Element Solution of Thermal Elastohydrodynamic Lubrication Problems

The derivation of fast, reliable, and accurate modeling procedures for the solution of thermal elastohydrodynamic lubrication problems is a topic of significant interest in the Tribology community. In this paper, a novel model order reduction technique is introduced for the analysis of thermal elastohydrodynamic lubrication problems. The method uses static condensation to reduce the size of the linear elasticity part within the overall matrix system, followed by a splitting algorithm to avoid the burden of solving a semi-dense matrix system. The results reveal the exactness of the proposed methodology, which does not introduce any additional model-reduction approximations to the overall solution. They also reveal the reduction in computational times, which is in the order of 10–20% for line contacts, while it is in excess of 50% for circular contacts. The robustness of the proposed method is displayed by using it to model some relatively highly loaded contacts whose numerical solution is known to be rather challenging.

Understanding the Influences of Multiscale Waviness on the Elastohydrodynamic Lubrication Performance, Part I: The Full-Film Condition

Understanding the responses of tribosystems to multiscale roughness is fundamental for the identification of the relevant roughness scales. This work used a point-contact elastohydrodynamic lubrication (EHL) problem as a representative tribosystem and artificially generated waviness with different amplitudes, frequencies, and directions to mimic the multiscale roughness. The amplitudes and frequencies are related to the feature geometry of smooth EHL problems. This work consists of Part I (this paper), focusing on the full-film condition, and Part II, focusing on the partial-film condition. Generated waviness is input to a transient thermal EHL model. The simulation is conducted 1600 times for different waviness parameters, loads, and speeds. Seven performance parameters are extracted: the minimum film thickness, maximum pressure, central film thickness, central pressure, mean film thickness, coefficient of friction (COF), and maximum temperature rise. The ratios of these parameters with and without waviness are plotted on the frequency–amplitude coordinate plane as contour maps. The influences of the amplitude, frequency, wave direction, load, and speed on the seven performance parameters are analyzed and summarized. The simulated data and plotted contour maps are provided to the readers in the Supplementary Material.

Influence of Manufacturing Error Tolerances on Thermal EHL Behavior of Gears

Due to the electrification of vehicles, new demands are being imposed on gears, which translates to the tolerances of manufacturing errors. However, not many studies treat the impact of manufacturing error combinations on the lubricant behavior of gear sets. Therefore, a simulation method is developed, including its derivation, discretization, and implementation. The method solves the thermal elasto-hydrodynamic lubrication (TEHL) problem, taking into account the varying temperature, viscosity, density, and cavitation of the lubricant. To account for manufacturing errors, the load distribution from a loaded tooth contact analysis (LTCA), developed by the authors, is used as input to the TEHL method. Comparison is made with a standard load distribution assumption, and a numerical example is used to show some preliminary results. The results show good agreement with results from other studies. It is shown that there is a great effect of manufacturing errors on the TEHL behavior, such as temperature, due to the change in load distribution such errors impose. It can be concluded that manufacturing errors of different tolerances have a great impact and that they should therefore be taken into consideration when analyzing gear set behavior and constructing gear sets for new applications.

Mixed EHL Problems: An Efficient Solution to the Fluid–Solid Coupling Problem with Consideration of Elastic Deformation and Cavitation

For transient mixed Elastohydrodynamic lubrication (EHL) problems, a novel solution is required to predict friction loss and wear in sliding or rolling parts. However, existing solutions have numerous limitations. In general, the lower the oil film thickness is, the more serious the non-linear problem is. This paper presents an efficient solution to tackle the non-linearity of the mixed EHL problem. The elastic deformation in the fluid–solid iteration coupling problem is divided into two parts: One is induced by the hydrodynamic pressure. This part of the deformation is obtained by the unsteady EHL-FBNS (Fischer–Burmeister–Newton–Schur) solver by considering both mass-conserving cavitation and elastic deformation. The other part of the deformation is introduced by the asperity contact pressure. It can be obtained by the Newton–Raphson method. After some limited iterations, the mixed EHL problems can be solved by evaluating the residual total pressure (including hydrodynamic pressure and asperity contact pressure). The proposed methodology was validated against the results from the published literature and applied to characterize the tribological performance of point contact with moving texturing. It appears that the developed method can be effectively used for tracking the tribological behavior of friction pairs.

An integrated finite volume framework for thermal elasto-hydrodynamic lubrication

Recent advances in computational methods and resources have fuelled numerical studies to explore novel techniques for solving thermal elasto-hydrodynamic lubrication (TEHL) problems. Commercial codes such as those that feature the Computational Fluid Dynamics (CFD) approach have gained much attention in the field of tribology due to the ability to tackle the limitations imposed by Reynolds equation assumptions and aptness in modelling complex geometries. However, the computational cost incurred by CFD software is significantly high due to the governing equations involved when solving the most general problem. The present contribution proposes an integrated finite-volume framework to solve TEHL problems to predict the lubrication performance of non-conformal contacts. Fluid flow effects are considered through the generalized Reynolds equation with the p−θ Elrod–Adams mass-conserving cavitation model to ensure the mass flow-rate conservation throughout the lubricated domain. The thermal behaviour of the lubricant film is predicted via the solution of the conservation of energy equation with appropriate boundary conditions for the fluid–solid interfaces. Novel partitioned iterative solution methods are integrated into the framework to handle the strong nonlinearities and improve the convergence of the coupled system of equations. Thermal and isothermal cases are presented and compared to results generated by existing CFD solvers and other experimental data to validate the proposed framework.

Fluid–Solid Interaction Modeling of Elastohydrodynamic Lubrication Point Contacts

Abstract Elastohydrodynamically lubricated point contact was investigated using a two-way partitioned fluid–solid interaction (FSI) model. ansys Mechanical finite element modeling software was used to compute elastic (and plastic) deformation of the solid bodies, while ansys fluent computational fluid dynamics software was used to model the fluid with the Navier–Stokes equations. The current model is not limited by Reynolds equation assumptions, allowing for the investigation of pressure, viscosity, and temperature variation across point contact elastohydrodynamic lubrication (EHL) films. Solid body material stress distribution and fluid behavior such as cavitation were also investigated. The details of model development are described. Validation of the model is presented across a range of loads and speeds for cases when the Reynolds equation is applicable. The results are in excellent agreement. Various slide-to-roll ratios were investigated considering a non-Newtonian fluid with thermal effects to characterize lubricant properties within the EHL film. Results demonstrate notable lubricant viscosity and temperature variations within the EHL film thickness both along and perpendicular to the rolling direction for cases with high slide-to-roll ratio. Cavitation was also considered, and cavitation bubble lengths were found to agree well with results found in open literature. Finally, the effects of material plasticity on solid body response were investigated. The FSI model developed in this research provides new insights on a classical EHL problem.

A Hydrodynamic Thrust Bearing Lubricated By A Non-Newtonian Giesekus Fluid

There exists a huge volume of studies of hydrodynamic and elastohydrodynamic lubrication problems for lubricants with Newtonian rheology. Lubricants with Newtonian rheology do not exhibit the usually observed experimentally behavior of having relatively high viscosity for low stresses and relatively low viscosity for high stresses. In this paper we extend the earlier conducted analysis of lubricants with a non-Newtonian Giesekus behavior for the case of thrust bearing modeling. The main goal of the paper is to obtain an analytical solution for a hydrodynamically thrust bearing lubricated by a fluid with the Giesekus rheology. This goal is achieved by careful application of perturbation methods. A three-term approximate analytical solution is obtained and its dependence on the problem input parameters is analyzed.

Two-dimensional generalized non-Newtonian EHL lubrication: Shear rate-based solution versus shear stress-based solution

Lubricant behaves non-Newtonian at high shear stress and high shear rate. The non-Newtonian shear behavior of oil such as shear-thinning, viscoelasticity, and limiting shear stress could have influences on almost all characteristics of an elastohydrodynamic lubrication (EHL) contact, that is, the central film thickness, the coefficient of friction, and the temperature rise in the lubricating film. For example, for lubricants of large molecular weight or of polymer blended ones, there can be inlet shear-thinning, which would reduce the EHL film thickness. For the EHL traction in a rolling/sliding EHL contact, it cannot be reasonably predicted without the consideration of non-Newtonian rheology. In EHL numerical studies, the non-Newtonian properties and the constitutive equations are expressed by the concept of generalized viscosity [Formula: see text], which can be either a function of shear rate [Formula: see text] or a function of shear stress [Formula: see text]. In this way, a non-Newtonian lubrication problem could be solved as a generalized Newtonian problem based on solvers for a Newtonian EHL problem. According to the function of the generalized viscosity [Formula: see text], numerical solutions can be classified into shear rate-based ones and shear stress-based ones. In this work, these two kinds of numerical solutions are revisited. And their efficiency is compared for a two-dimensional (2D) non-Newtonian point contact EHL problem (here 2D means non-Newtonian flow in both the x and y directions). Results show that the shear rate-based numerical solution has a higher efficiency than the shear stress-based one. The shear rate-based 2D generalized Newtonian method is more suitable to analyze multiple EHL contacts in angular contact ball bearings and gears with complex 2D flow and/or transient EHL lubrication problems.

Access to computers

In one of Duncan Dowson’s talks on the early attempts to solve the elastohydrodynamic lubrication problem, he commented that progress only became possible when he and Gordon Higginson were granted private access to the University computer at weekends. And how these words brought back memories! For John Tripp and I could never have solved our numerical problem without the courtesy of the Norwalk State Technical College allowing us access to its computer out of term. That was in 1964. In this century, such a story is hard to believe, when every researcher has on his own desk, for his own use, a computer more powerful than either of the two referred to above. It seems worth recalling how computing has changed in my scientific lifetime.

Computational Efficiency Improvement of Dimple Textured Hydrodynamic Journal Bearing Using Progressive Mesh Densification Method

Abstract There is a considerable amount of study carried out on textured hydrodynamic bearings. The numerical solution of textured bearings is a matter of concern for the researchers. There are several methods used to estimate the performance parameters of textured bearings. However, progressive mesh densification (PMD) method is not yet used for textured bearings while it has been used for mixed elastohydrodynamic lubrication (EHL) and thermo-EHL problems. In the present analysis, the PMD method is implemented to estimate the performance parameters of the textured journal bearing. It is compared with the multigrid and the fixed mesh methods and found to be very effective in improving computational efficiency.

Formulation to Calculate Isothermal, Non-Newtonian Elastohydrodynamic Lubrication Problems Using a Pressure Gradient Coordinate System and Its Verification by an Experimental Grease

This paper presents a formulation of point contact elastohydrodynamic lubrication analysis for an isothermal, non-Newtonian flow. A coordinate system of the pressure gradient was employed herein. A Couette flow and a Poiseuille flow were considered along the directions of the zero and non-zero pressure gradients, respectively. The Poiseuille flow velocity was assumed to be represented by a 4th-order polynomial of z along the film thickness direction. The Couette flow velocity was assumed to be represented by a linear function of z. Subsequently, the modified Reynolds equation, which contains an equivalent viscosity, was obtained. Using Bauer’s rheological model, the formulation presented in this study was applied to a grease that has been previously experimented upon. The results of previous studies were compared with those of the present study and a reasonable agreement was noted. The distribution of the equivalent viscosity showed a notable difference from that of Newtonian flow. The formulation can be incorporated easily to the usual elastohydrodynamic lubrication calculation procedure for Newtonian flow. The method can be easily applied to other non-Newtonian rheological models. The equivalent viscosity can be calculated using the one-parameter Newton-Raphson’s method; as a result, the calculation can be performed within a reasonable time.

Fluid–Structure Interaction Modeling of Elastohydrodynamically Lubricated Line Contacts

Abstract This paper presents a partitioned fluid–structure interaction (FSI) solver to model elastohydrodynamic lubrication (EHL) of line contacts. The FSI model was constructed using the multiphysics simulation software ansys, wherein an iterative implicit coupling scheme is implemented to facilitate the interaction between fluid and solid components. The model uses a finite volume method (FVM) based computational fluid dynamics (CFD) solver to determine the lubricant flow behavior using the Navier–Stokes equations. Additionally, the finite element method (FEM) is utilized to model the structural response of the solid. Fluid cavitation, compressibility, non-Newtonian lubricant rheology, load balance algorithm, and dynamic meshing were incorporated in the FSI model. The pressure and film thickness results obtained from the model are presented for a wide range of loads, speeds, slide to roll ratios (SRR), surface dent, material properties (elastic plastic), etc. The model presents a detailed understanding of EHL contacts by removing any assumptions relative to the Reynolds equation. It provides the (i) two-dimensional variation of pressure, viscosity, etc., in the fluid and (ii) stress, elastic/plastic strain in the solid, simultaneously. The FSI model is robust, easy to implement, and computationally efficient. It provides an effective approach to solve sophisticated EHL problems. The FSI model was used to investigate the effects of surface dents, plasticity and material inclusions under heavily loaded lubricated line contacts as can be found in gears and rolling element bearings. The results from the model exhibit excellent corroboration with published results based on the Reynolds equation solvers.

Concise Data Set Formulation for Dynamically Loaded Conformal Elastohydrodynamic Lubrication Problems

AbstractThis paper introduces a concise data set formulation for efficient modeling of dynamically loaded conformal elastohydrodynamic lubrication (EHL) problems. The data set represents the structural elasticity of the bearing members and is constructed independently of the lubricant film model. Data set construction involves modification of a previously published mode-based EHL formulation such that the resulting structural information is insensitive to changes in finite-element mesh density and thus to the modeling process itself. Curve-fitted expressions of modal information are introduced for elastic structures, which otherwise would normally be represented by large structural matrices. A data set is formulated for the sample case of a dynamically loaded big-end connecting-rod bearing, and the resulting bearing performance agrees well with previously published node- and mode-based EHL methods.

Numerical Analysis of Grease Film Thickness and Thickener Concentration in Elastohydrodynamic Lubrication of Point Contacts

This article presents a numerical analysis of elastohydrodynamic lubrication (EHL) with grease in point contacts to predict the grease film thickness at low speeds, which can increase with decreasing speed and exceed the base oil film thickness by orders of magnitude. The grease film thickness is obtained by solving the EHL problem, taking grease flow as a single-phase flow with a non-Newtonian viscosity. The continuity equation for thickener is derived, taking grease flow as a two-phase flow of base oil and thickener and the network structure of the thickener as both a porous medium and a non-Newtonian fluid. The flow rate of the thickener network is obtained as the grease flow rate subtracted by the Darcy flow rate of the base oil. The thickener concentration is obtained by solving the continuity equation for the thickener. Numerical results show that the increase in film thickness at low speeds is due to an increase in the equivalent viscosity in the inlet of the contact, which is due to a decrease in the shear rate and an increase in the thickener concentration. At low speeds, base oil is more easily squeezed out of the inlet of the contact than the thickener network, which leads to an increase in the thickener concentration, because the shear stress due to the Newtonian flow of base oil decreases with decreasing the shear rate, whereas the yield stress of the thickener network is independent of the shear rate. A reasonable agreement between the numerical and experimental results validates the present model.

On Waviness and Two-Sided Surface Features in Thermal Elastohydrodynamically Lubricated Line Contacts

Machine components are designed to endure increasingly severe operating conditions due to the strive for improved energy efficiency of mechanical systems. Consequently, lubricated non-conformal contacts must rely on thin lubricant films where the influence of surface topography on the lubricating conditions becomes significant. Due to the complexity of the multiphysical problem, approximate assumptions are often employed to facilitate numerical studies of elastohydrodynamically lubricated (EHL) contacts. In this work, the rough, time dependent, thermal EHL problem is solved with focus on two main analyses. The first analysis focuses on the influence of sinusoidal roughness and the difference between a thermal non-Newtonian approach and an isothermal Newtonian approach. The second analysis is focused on the lubricating mechanisms taking place when two-sided surface features overtake within the thermal EHL contact. The results indicate that the film thickness in the outlet of the contact may be significantly overestimated by an isothermal Newtonian approach and that differences in the high-pressure region may also occur due to viscosity variations in the inlet of the contact. Moreover, for the studied two-sided surface features, it became evident that not only the surface feature combination but also the overtaking position influence the film thickness and pressure variations significantly.