Solution Of Elastohydrodynamic Lubrication Research Articles

Lubrication Prediction of Sphere‐Gradient Coated Half Space Interfaces

ABSTRACTFunctionally graded coating (FGC) has played a pivotal role in numerous engineering applications owing to its exceptional properties. This work proposes a novel elastohydrodynamic lubrication (EHL) model with FGC, in which the elastic deformation and stress are computed using influence coefficients (ICs) and discrete convolution‐fast Fourier transform (DC‐FFT) algorithm. Comparisons are made with homogeneous EHL solutions and finite element analysis (FEA) to validate its accuracy. The study systematically explores how coating elastic modulus, coating thickness and substrate elastic modulus influence contact and lubrication behaviours. The developed model is expected to establish a theoretical framework for FGC material design, enhancing the performance of friction pairs.

Effects of Solid Temperature and Ambient Pressure on Thermal Elastohydrodynamic Lubrication Solutions

Effects of Solid Temperature and Ambient Pressure on Thermal Elastohydrodynamic Lubrication Solutions

An Improved Load Distribution Model for Gear Transmission in Thermal Elastohydrodynamic Lubrication

The gear drive generally operates in elastohydrodynamic lubrication (EHL) contacts, and the existence of oil film effectively reduces wear and improves transmission stability. However, little research has been devoted to studying the effect of lubrication characteristics on load distribution of gear transmissions. In order to investigate the coupling effect between the lubrication behavior and load distribution, an analytical load distribution model suitable for EHL contact spur gear pairs is proposed. The non-Newtonian transient thermal EHL solution, flexibility of meshing teeth, structural coupling deformation of the gear body and extended tooth contact are considered in the deformation compatibility condition for iteratively solving the load distribution. A parametric analysis is performed to determine the influence of load torque and rotation speed on load sharing ratio and loaded static transmission error. The transient lubrication behaviors based on the proposed load distribution model is compared with that obtained from the traditional model. A series of comparisons with different models demonstrated the correctness, significance and generality of the present model. The results show that it is necessary to consider the thermal EHL calculation into the iterative solution procedure of load distribution model for EHL contact gear pairs. The proposed model is a useful supplement for an accurate study of thermal EHL characteristics of gear transmissions.

The influence of surface topography on mixed plasto-elastohydrodynamic lubrication in point contacts

Surface topography plays an important role in mixed lubrication. However, the influence of the surface topography's morphological characteristics on lubrication performance is still not fully understood. In this article, we employ digital filtering and the Johnson transformation system, and we use a mixed plasto-elastohydrodynamic lubrication model to simulate the lubricated contact between rough spherical surfaces with different morphological characteristic parameters. The influence of skewness, kurtosis, and the wavelength factor, that is, the ratio between the autocorrelation lengths in the transversal and longitudinal directions, on contact pressure, film thickness, and von Mises (subsurface) stress, is examined with the mixed plasto-elastohydrodynamic lubrication model. The results confirm that plastic deformation leads to lower pressure distribution, distributed over a larger contact area than the pure elastohydrodynamic lubrication solution. Moreover, it is found that an increase in the kurtosis may improve the lubrication performance, while the opposite is true for the skewness and the wavelength factor. We believe that the insights obtained by means of the numerical simulations presented herein, would facilitate the design and manufacturing processes of the surfaces used for machine elements operating in the mixed plasto-elastohydrodynamic lubrication regime.

Squeeze lubrication between soft solids: A numerical study

Squeezing a lubricating film between viscoelastic solids is a process with many applications, ranging from biomechanics to industrial engineering. The problem is addressed by means of an innovative numerical strategy coupling a finite difference solver for the lubricant fluid dynamics and a Boundary Element approach, which provides the deformation field in the solid. Results show marked differences compared to classical elasto-hydrodynamic lubrication (EHL): Pressure and film thickness depend, in fact, on the material viscoelastic relaxation, peaking at the two edges of the lubricated contact area. This implies, also for the minimum and central thickness values, time-dependent trends that significantly deviate from EHL solution and, thus, point out the necessity of accounting for the actual viscoelastic rheology of the lubricated solids.

Duncan Dowson and elastohydrodynamic lubrication at Leeds University

This paper retraces the fascinating developments made by Professor Dowson at Leeds University in the field of elastohydrodynamic lubrication, starting from the early years of elastohydrodynamic lubrication solutions to his most recent contribution to biotribology and mixed lubrication.

An Improved Dynamic Transmission Error Model Applied on Coupling Analysis of Gear Dynamics and Elastohydrodynamic Lubrication

Abstract In order to study the coupling effect of cylindrical gear dynamics and elastohydrodynamic lubrication (EHL), based on dynamic theory, a dynamic model of a six degrees-of-freedom (6DOF) coupled system is established. Based on the numerical solution of EHL, an improved dynamic transmission error (DTE) model was established. The oil film stiffness, oil film damping, and center oil film thickness obtained by the numerical solution were used in the gear dynamics analysis. The dynamics and EHL characteristics of the gear system are analyzed and compared with the general model. The results show that by using the improved DTE model, the comprehensive stiffness and comprehensive damping of the gear increase and fluctuate slightly. The amplitude of the tooth surface meshing force and dynamic response decreases. Under the action of tooth surface meshing force, the oil film pressure and thickness show oscillation characteristics.

Influence of Lubricant Physical Property Models on Thermal Elastohydrodynamic Lubrication Solutions

The influence of changes in the physical properties of lubricants on thermal elastohydrodynamic lubrication solutions is examined numerically at the nominal line contact for both Newtonian and non-Newtonian fluids. Specific heat, thermal conductivity, density, and viscosity were considered as functions of temperature and pressure for polyalphaolefin, polyglycol, and mineral oils. It was found that, when considering the physical and rheological properties of lubricants individually, the solutions were over- or under-estimated. The thermal conductivity formula mostly corresponds to solutions for both fluids. The effects of changes in the physical properties of non-Newtonian lubricants were shown to be less than those of Newtonian lubricants. Near-identical qualitative behaviors occurred regardless of oil type under these lubricant models.

Numerical Solution of Elastohydrodynamic Lubrication for Sliding/Rolling Bearing for Non-newtonian Lubricant

There is always a demand in the industry sector to increase the efficiency of machine components to reduce wear and tear. This paper presents the numerical solution to the study of Elastohydrodynamic lubrication point contact for sliding/rolling bearing where the viscosity of the lubricant is non-Newtonian. The assumption that a lubricant is Newtonian reduces validation of the model hence the Reynolds-Eyring model in this research will incorporate the non-Newtonian nature of the lubricant of the bearing. The mathematical model comprises of Reynold-Eyring equation, film thickness, load balance, lubricant viscosity and lubricant density equations together with their boundary conditions. The Reynolds-Eyring equation governing the flow is non-linear hence the finite difference method numerical technique is used to discretize it together with the other two dimensional equations. These equations are solved simultaneously and Matlab software is used simulate the results. The film thickness and pressure profiles with various loads and speeds are presented. The findings note that an increase in load lowers the pressure and film thickness while an increase in the speed results to a direct increase in pressure and film thickness. A pressure spike is also noted at the exit of the bearing.

Numerical analysis of cam and follower based on the interactive design approach

The contact between the cam and follower is considered as one of the most complicated problems from the lubrication point of view. The contact in this elastohydrodynamic lubrication (EHL) problem undergoes extreme variation conditions of different parameters. These include the load variation, geometry at the contact point and sliding speed. This paper presents an EHL solution for the contact problem between cam and chamfered follower (originally flat faced). The model of solution is point contact in order to accurately simulate the chamfering of the follower. The solution of Reynolds equation considers the non- Newtonian oil behavior in the calculation of the flow factors. The interactive design approach used in this paper focused mainly on the effect of chamfer as well as the other general parameters of the mechanism. The results revealed that chamfering of the follower in the axial direction has considerable effects on the performance of the mechanism. The linear modification causes significant rise in the maximum pressure and extreme thinning in the film thickness.

Finite difference Wavelet–Galerkin method for the numerical solution of elastohydrodynamic lubrication problems

The use of compactly supported wavelet functions has become increasingly popular in the development of numerical solutions for differential equations, especially for problems with local high gradient. Daubechies wavelets have been successfully used as base functions in several schemes like the Wavelet–Galerkin Method, due to their compact support, orthogonality, and multi-resolution properties. Another advantage of wavelet-based methods is the fact that the calculation of the inner products of wavelet basis functions and their derivatives can be made by solving a linear system of equations, thus avoiding the problem of approximating the integral by some numerical method. These inner products were defined as connection coefficients and they are employed in the calculation of stiffness, mass and geometry matrices. Solving connection coefficients in the Wavelet–Galerkin Method is complicated. In this work, Finite Difference Wavelet–Galerkin Method is developed for the numerical solution of elastohydrodynamic lubrication (EHL) problems. This approach enables the use of the finite difference and multiresolution analysis. Using this method numerical solution (pressure (P) and film thickness (H)) of the EHL problem is obtained and presented in comparison with the finite difference solution in tables and figures. Finite difference Wavelet–Galerkin method is easier to implement than the Wavelet–Galerkin Method and it gives fast and accurate solution.

Alternative calculation on transient elasto-hydrodynamic lubrication

PurposeThe purpose of this study is to propose a new method to solve transient elasto-hydrodynamic lubrication (EHL) problem.Design/methodology/approachFirst, the steady-state EHL solution is modified so that the elastic deformation theory is combined with oil film stiffness distribution instead of steady-state Reynolds equation. Second, subsequent dynamic EHL procedure develops, recursively using transient distributed oil film stiffness and damping, where each time-marching solution is iteratively searched by ensuring both oil film force growth and elastic deformation update for each load increment.FindingsThis method increases calculation speed and provides both distributed EHL stiffness and damping for transient regimes.Originality/valueThis method is of interest for fast applications such as rolling bearings or gears.

On Transient EHL of a Skew Roller Subjected to a Load Impact in Rolling Bearings

Based on the non-steady state operating condition in machine elements, numerical analysis of a transient elastohydrodynamic lubrication (EHL) finite line contact between a skewed roller and an outer race in cylindrical roller bearings was carried out, and a complete numerical solution of skewed roller pairs EHL under the transient condition was obtained. The effects of the load impact, together with the skewing angle impulses on the lubricating performance of skew roller pairs were discussed. Results show that, different from the steady state, the transient effect of the skew roller lubrication is mainly governed by the skew angle impulse, and the load impact. The film dimple is generated during the load impact, or the skewing angle impulse due to the normal approach velocity of the film. Compared to that of the ideal roller, the minimum film thickness decreases due to the roller skew when the transient load happens. Variation in the skewing angle leads to contrary distribution of the film thickness at the two half parts of the roller. Meanwhile, it can decrease the minimum film thickness and be harmful to the lubrication compared to the steady state. Consequently, the transient effect in the process of lubrication of skew roller pairs should not be neglected.

Progressive Mesh Densification Method for Numerical Solution of Mixed Elastohydrodynamic Lubrication

Numerical solution of mixed elastohydrodynamic lubrication (EHL) is of great importance for the study of lubrication formation and breakdown, as well as surface failures of mechanical components. However, converged and accurate numerical solutions become more difficult, and solution process with a fixed single discretization mesh for the solution domain appears to be quite slow, especially when the lubricant films and surface contacts coexist with real-machined roughness involved. Also, the effect of computational mesh density is found to be more significant if the average film thickness is small. In the present study, a set of sample cases with and without machined surface roughness are analyzed through the progressive mesh densification (PMD) method, and the obtained results are compared with those from the direct iteration method with a single fixed mesh. Besides, more numerical analyses with and without surface roughness in a wide range of operating conditions are conducted to investigate the influence of different compound modes in order to optimize the PMD procedure. In addition, different initial conditions are used to study the effect of initial value on the behaviors of this transient solution. It is observed that, no matter with or without surface roughness considered, the PMD method is stable for transient mixed EHL problems and capable of significantly accelerating the EHL solution process while ensuring numerical accuracy.

On the Numerical Accuracy of Rough Surface EHL Solution

Numerical solution of rough surface elastohydrodynamic lubrication (EHL) is of great importance. In recent years, research efforts have been focused on deterministic modeling, because it is proven to be capable of predicting detailed contact and lubrication characteristics based on measured three-dimensional machined surface topography in a wide range of operating conditions. The accurate calculation of roughness derivatives, ∂S/∂X and ∂S/∂T, is found to be crucial for numerically solving EHL problems, especially if machined roughness with high-frequency components is involved. When discretized rough surfaces are employed, one may have to handle three different discretization grids, one for the stationary solution domain of the Reynolds equation and the other two for the moving rough surfaces in contact. Two numerical ways can be employed to fulfill the computation of ∂S/∂X and ∂S/∂T. One is to interpolate the topographic heights into the solution domain grid and then conduct the derivation calculations there. The other is to do derivations first in the surface grids and then interpolate the obtained derivatives into the solution mesh. In order to compare these two ways based on an accuracy analysis, a transverse sinusoidal rough surface is exploited and the effects of mesh spacing, differential scheme, interpolation method, and roughness wavelength on numerical errors of ∂S/∂X and ∂S/∂T are investigated. It is found that the appropriate way to minimize the errors is to ensure that the surface grids are considerably denser than that of the solution domain and to conduct derivation calculation first on the surface grids. A densified surface mesh may lead to a great reduction in numerical errors without causing any significant increase in the computing time. Densification of the solution domain mesh, on the other hand, is more difficult because it would result in a large increase in computational burden. It is also found that high-order differential schemes and interpolation methods are helpful to improve accuracy. Large roughness wavelengths lead to smaller numerical errors, but roughness amplitude has no influence on numerical accuracy.

Analysis of Surface Scratch in Finite Line Contact EHL

In this paper, the phenomenon of roller scratch in Elastohydrodynamic lubrication(EHL) state is simulated successfully. A complete thermal EHL solutions of finite roller with scratch are obtained. Comparasions between current numerical film contours and Cameron’s optical interferometry graph shows satisfactory agreement. The characteristics of pressure, filmthickness as well as temperature distributions are discovered numerically. It could be concluded that surface scratch will generate a pressure increase, a high temperature and a thin film distributions on both outsides of the scratch, as well as a pressure drop, a low temperature and a thicker film distributions at the inside location of the scratch. Therefore, it will produce a local sharp maximum stress concentration and may possiblly lead to lubrication failure, which will accelerate the process of surface fatigue.

Fast and reduced full-system finite element solution of elastohydrodynamic lubrication problems: Line contacts

This paper presents a reduced full-system finite element solution of elastohydrodynamic lubrication (EHL) problems. It aims to demonstrate the feasibility of this approach by applying it to the simple isothermal Newtonian line contact case. However the proposed model can be extended to more complex situations. This model is based on a full-system finite element resolution of the EHL equations: Reynolds, linear elasticity and load balance. A reduced model is proposed for the linear elasticity problem. For this, three different techniques are tested: the classical ''modal reduction'' and ''Ritz-vector'' methods and a novel ''EHL-basis'' method. The reduction order in the first two appears to be insufficient and a large number of degrees of freedom is required in order to attain an acceptable solution. On the other hand, the ''EHL-basis'' method shows up to be much more efficient, requiring only a few degrees of freedom to compose the elastic deformation of the solid components. In addition, a comparison with the full model shows an order of magnitude execution time gain with errors of the order of only 1%% for the central and minimum film thicknesses.

Bio–Based Lubricants for Numerical Solution of Elastohydrodynamic Lubrication

This paper presents a numerical solution of elastohydrodynamic lubrication (EHL) problem in line contacts which is modeled through an infinite cylinder on a plane to represent the application of cylindrical roller bearing. In this work, the contact between roller element and raceway of outer ring of the cylindrical roller bearing is simulated using vegetable oils as bio-based lubricants. Temperature is assumed to be constant at 40oC. The results show that the EHL pressure for all vegetable oils was increasing from inlet flow until the center, then decrease a bit and rise to the peak pressure. The shapes of EHL film thickness for all tested vegetable oils are almost flat at contact region.

Effect of Impact Load on Transient Elastohydrodynamic Lubrication of Involute Spur Gears

Nonstationary elastohydrodynamic lubrication (EHL) of an involute spur gear is a very complex problem. A full transient EHL solution of an involute spur gear is obtained by utilizing the multigrid method, which takes the variation in equivalent curvature, entrainment velocity, and load with time along the line of action into consideration. The lubricant thermal and rheological effects are ignored and the gear teeth are assumed to be rigid in the model as far as tooth flexure is concerned. The influences of load spectrum and impact on EHL are analyzed in this article. Over a meshing cycle of a tooth pair, initially the load is carried by two contacting tooth pairs and then there is a transition to single tooth pair, followed by a final transition to shared loading between two tooth pairs. The impact load when the teeth come into action is taken into consideration. The results show that the transient effects have a strong influence on the maximum pressure and minimum film thickness. The load spectrum plays an important role in EHL of gears.

On the linear finite element analysis of fully coupled point contact elastohydrodynamic lubrication problems

The fully coupled approach for the solution of elastohydrodynamic lubrication point contact problems requires the numerical solution of the elasticity problem on a large 3D domain. A sufficiently fine computational mesh is required to obtain the elastic deformation solution to the necessary accuracy, and hence, a sufficiently accurate elastohydrodynamic lubrication point contact solution. This article discusses the accuracy of an elastohydrodynamic lubrication point contact solution over different finite element meshes. We present a family of efficient 3D meshes which can be used to calculate accurate elastohydrodynamic lubrication point contact solutions at a minimal computational cost. This article also illustrates the fact that the unstructured hierarchical meshes can lead to a poor quality elastohydrodynamic lubrication solution unless an appropriate post-processing, smoothing technique is applied.