An Efficient, Robust, Multi-Level Computational Algorithm for Elastohydrodynamic Lubrication

1989 ◽  
Vol 111 (2) ◽  
pp. 193-199 ◽  
Author(s):  
L. Chang ◽  
T. F. Conry ◽  
C. Cusano
Keyword(s):  
Computational Algorithm ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Contact Problems ◽  
Working Environment ◽  
Ehd Lubrication ◽  
Wide Range ◽  
Direct Iteration ◽  
Multi Level ◽  
And Storage

A new computational algorithm is developed for the numerical analysis of elastohydrodynamic (EHD) lubrication problems. This algorithm combines direct-iteration, Newton-Raphson, and multigrid methods into one working environment. Accurate solutions for a wide range of steady-state, line-contact problems are obtained with a relatively small number of numerical operations. The algorithm can be used to efficiently simulate transient processes in EHD lubrication. It can also be extended to solve point-contact problems with high computational and storage efficiency.

Solving EHL Problems Using Iterative, Multigrid, and Homotopy Methods

1999 ◽  
Vol 121 (1) ◽  
pp. 28-33 ◽  
Author(s):  
Elyas Nurgat ◽  
Martin Berzins ◽  
Laurence Scales
Keyword(s):  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Grid Method ◽  
Contact Problems ◽  
Test Problems ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Future Developments ◽  
Relaxation Scheme ◽  
Highly Nonlinear

The numerical solution of ElastoHydrodynamic Lubrication (EHL) point contact problems requires the solution of highly nonlinear systems of equations which pose a formidable computational challenge. Multigrid methods provide one efficient approach. EHL problems solved using a single grid and multigrid will be compared and contrasted with a homotopy method which works on the concept of deforming one problem into another by the continuous variation of a single parameter. Both the multigrid and the single grid method employ a new relaxation scheme. Numerical results on demanding test problems will be used to compare these methods and suggestions for future developments to produce robust solvers will be made.

Numerical Solution of Mixed Thermal Elastohydrodynamic Lubrication in Point Contacts With Three-Dimensional Surface Roughness

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Xiaopeng Wang ◽  
Yuchuan Liu ◽  
Dong Zhu
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Three Dimensional ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Lubricant Film ◽  
Operating Conditions ◽  
Thickness Variation ◽  
Wide Range ◽  
Film Lubrication

Elastohydrodynamic lubrication (EHL) is a common mode of fluid-film lubrication in which many machine elements operate. Its thermal behavior is an important concern especially for components working under extreme conditions such as high speeds, heavy loads, and surfaces with significant roughness. Previous thermal EHL (TEHL) studies focused only on the cases with smooth surfaces under the full-film lubrication condition. The present study intends to develop a more realistic unified TEHL model for point contact problems that is capable of simulating the entire transition of lubrication status from the full-film and mixed lubrication all the way down to boundary lubrication with real machined roughness. The model consists of the generalized Reynolds equation, elasticity equation, film thickness equation, and those for lubricant rheology in combination with the energy equation for the lubricant film and the surface temperature equations. The solution algorithms based on the improved semi-system approach have demonstrated a good ability to achieve stable solutions with fast convergence under severe operating conditions. Lubricant film thickness variation and temperature rises in the lubricant film and on the surfaces during the entire transition have been investigated. It appears that this model can be used to predict mixed TEHL characteristics in a wide range of operating conditions with or without three-dimensional (3D) surface roughness involved. Therefore, it can be employed as a useful tool in engineering analyses.

Direct Observations of Emulsion Flow in Elastohydrodynamically Lubricated Contacts

2006 ◽  
Vol 128 (3) ◽  
pp. 619-623 ◽  
Author(s):  
Haixia Yang ◽  
Steven R. Schmid ◽  
Ronald A. Reich ◽  
Thomas J. Kasun
Keyword(s):  
High Speed ◽  
Direct Method ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Video Camera ◽  
Low Speed ◽  
Digital Video Camera ◽  
Wide Range ◽  
Emulsion Flow ◽  
Side Flow

The lubrication mechanisms with oil-in-water emulsions have been extensively investigated based on the measurements of film thickness and/or tractions in the past few decades. However, direct observation of the emulsion flow, as a more direct method of evaluating suggested explanations, has been greatly restricted by the available instruments, especially the cameras used in collaboration with high-speed bearing simulators. In this paper, a newly devised digital video camera and a microscope were used to directly observe the emulsion flow in an elastohydrodynamic lubrication (EHL) inlet region at a wide range of speeds (0.012m∕s up to 1.5m∕s). Both EHL line and point contacts were considered. Previous observations of low speed oil droplet “stay,” “reverse,” and “penetration” behavior for low-speed line contact were confirmed and extended into high-speed line and point cases, and the results were compared with point contact where significant side flow was observed. Three tight emulsions with different mean droplet sizes were examined on an EHL rig to clarify the droplet behavior and investigate the effect of droplet size on entrainment.

EHL Circular Contact Film Thickness Correction Factor for Shear-Thinning Fluids

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Punit Kumar ◽  
M. M. Khonsari
Keyword(s):  
Film Thickness ◽  
Correction Factor ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Shear Thinning ◽  
Correction Factors ◽  
Shear Thinning Fluids ◽  
Pure Rolling ◽  
Wide Range ◽  
Circular Contact

An extensive set of full elastohydrodynamic lubrication point contact simulations has been used to develop correction factors to account for the effect of shear-thinning lubricant behavior on the central and minimum film thickness in circular contacts under pure rolling condition. The film thickness for a shear-thinning lubricant can be easily obtained by dividing the corresponding Newtonian film thickness by the appropriate correction factor. Comparisons of the film thickness values obtained using the correction factors have been matched with the published experimental results pertaining to shear-thinning lubricants with a variety of realistic flow and piezoviscous properties under a wide range of operating speed. The good agreement between them establishes the validity and versatility of the correction factors developed in this paper.

Effect of Stiff Coatings on EHL Film Thickness in Point Contacts

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Yuchuan Liu ◽  
Q. Jane Wang ◽  
Dong Zhu
Keyword(s):  
Film Thickness ◽  
Coating Thickness ◽  
Performance Enhancement ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Thickness Variation ◽  
Grand Challenge ◽  
Maximum Increase ◽  
Wide Range ◽  
Minimum Film Thickness

Coatings are widely used for interface performance enhancement and component life improvement, as well as for corrosion prevention and surface decoration. More and more mechanical components, especially those working under severe conditions, are coated with stiff (hard) thin coatings. However, the effects of coatings on lubrication characteristics, such as film thickness and friction, have not been well understood, and designing coating for optimal tribological performance is a grand challenge. In this paper, the influences of coating material properties and coating thickness on lubricant film thickness are investigated based on a point-contact isothermal elastohydrodynamic lubrication (EHL) model developed recently by the authors. The results present the trend of minimum film thickness variation as a function of coating thickness and elastic modulus under a wide range of working conditions. Curve fitting of numerical results indicates that the maximum increase in minimum film thickness, Imax, and the corresponding optimal dimensionless coating thickness, H2max, can be expressed in the following forms: Imax=0.769M0.0238R20.0297L0.1376exp(−0.0243ln2L) and H2max=0.049M0.4557R2−0.1722L0.7611exp(−0.0504ln2M−0.0921ln2L). These formulas can be used to estimate the effect of coatings on film thickness for EHL applications.

A Generalized Thermal EHL Model for Point Contact Problems

2008 ◽  
Author(s):  
Yuchuan Liu ◽  
Q. Jang Wang ◽  
Dong Zhu ◽  
Fanghui Shi
Keyword(s):  
Surface Temperature ◽  
Thermal Model ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Contact Problems ◽  
Three Dimensions ◽  
Thermal Ehl ◽  
Generalized Reynolds Equation

A generalized thermal elastohydrodynamic lubrication (TEHL) model for point contact problems is developed based on an isothermal generalized Newtonian elastohydrodynamic (EHL) model recently developed. The thermal model couples FDM for lubricant energy equation and the DC-FFT method for surface temperature integration. A generalized Reynolds equation is derived considering the change of viscosity with respect to temperature, pressure and shear in three dimensions. Numerical cases are conducted to verify the model.

Elastohydrodynamic lubrication of a circular point contact for a compliant layered surface bonded to a rigid substrate Part 2: Numerical results

2000 ◽  
Vol 214 (3) ◽  
pp. 281-289 ◽  
Author(s):  
Z. M. Jin
Keyword(s):  
Film Thickness ◽  
Layer Thickness ◽  
Poisson’S Ratio ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Poisson's Ratio ◽  
Contact Radius ◽  
Rigid Substrate ◽  
Circular Point ◽  
Wide Range

Both the theoretical formulation and the numerical analysis of the elastohydrodynamic lubrication problem of a circular point contact of a compliant layered surface firmly bonded to a rigid substrate have been present in the earlier paper, Part 1. The numerical method is applied, in this paper, to a compliant layered surface firmly bonded to a rigid substrate. The results of the film thickness and pressure distribution are presented for a wide range of ratios of the contact radius to the layer thickness and Poisson's ratio. It has been shown that the film thickness for a layered surface can be predicted from the semi-infinite solid assumption when the ratio of the contact radius to the layer thickness is less than or equal to 0.25. Furthermore, it has been demonstrated that, for a layered surface with Poisson's ratio equal to 0.4, the elastohydrodynamic solutions based on the simple constrained column model are reasonably accurate when the contact radius is larger than or equal to the layer thickness. General non-dimensional solutions of the minimum and central film thicknesses have been presented using the Moes load and film thickness parameters as a function of the ratio of the contact radius to the layer thickness and Poisson's ratio. All the numerical solutions of both the central and the minimum (along the centre of contact in the entraining direction) film thicknesses have been curve fitted using a least-squares technique. A normal human hip joint has been chosen as an example to illustrate the application of the present study.

Non-Newtonian Thermal Analyses of Point EHL Contacts Using the Eyring Model

2005 ◽  
Vol 127 (1) ◽  
pp. 70-81 ◽  
Author(s):  
Xiaoling Liu ◽  
Ming Jiang ◽  
Peiran Yang ◽  
Motohiro Kaneta
Keyword(s):  
Effective Viscosity ◽  
Numerical Solutions ◽  
Thermal Analyses ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Contact Problems ◽  
Point Contacts ◽  
Eyring Model ◽  
Thermal Ehl

A non-Newtonian numerical solution system for the thermal elastohydrodynamic lubrication (EHL) problems in point contacts has been developed. The Eyring rheology model has been used to describe the non-Newtonian flow of the lubricant. An effective viscosity has been defined for the Eyring fluid. The Newtonian solver can be applied easily to the non-Newtonian problems when the viscosity of the Newtonian fluid is replaced by the effective viscosity. A novel technique for the determination of the effective viscosity is proposed. Numerical solutions for the conventional point contact and normally crossing cylinders contact problems are presented and the effects of the entraining velocity, the load, the slide-roll ratio, and the characteristic shear stress of the Eyring fluid on the lubricating performance are discussed. The results indicate that the non-Newtonian thermal EHL theory predicts more realistic film temperatures and traction coefficients.

scholarly journals Recent Insights into Anthocyanin Pigmentation, Synthesis, Trafficking, and Regulatory Mechanisms in Rice (Oryza sativa L.) Caryopsis

Biomolecules ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 394 ◽  
Author(s):  
Enerand Mackon ◽  
Guibeline Charlie Jeazet Dongho Epse Mackon ◽  
Yafei Ma ◽  
Muhammad Haneef Kashif ◽  
Niyaz Ali ◽  
...  
Keyword(s):  
Food Industry ◽  
Anthocyanin Biosynthesis ◽  
Oryza Sativa L ◽  
Anthocyanin Synthesis ◽  
Pigmented Rice ◽  
Complex Processes ◽  
Natural Colorants ◽  
Wide Range ◽  
Anthocyanin Production ◽  
And Storage

Anthocyanins are antioxidants used as natural colorants and are beneficial to human health. Anthocyanins contribute to reactive oxygen species detoxification and sustain plant growth and development under different environmental stresses. They are phenolic compounds that are broadly distributed in nature and are responsible for a wide range of attractive coloration in many plant organs. Anthocyanins are found in various parts of plants such as flowers, leaves, stems, shoots, and grains. Considering their nutritional and health attributes, anthocyanin-enriched rice or pigmented rice cultivars are a possible alternative to reduce malnutrition around the globe. Anthocyanin biosynthesis and storage in rice are complex processes in which several structural and regulatory genes are involved. In recent years, significant progress has been achieved in the molecular and genetic mechanism of anthocyanins, and their synthesis is of great interest to researchers and the scientific community. However, limited studies have reported anthocyanin synthesis, transportation, and environmental conditions that can hinder anthocyanin production in rice. Rice is a staple food around the globe, and further research on anthocyanin in rice warrants more attention. In this review, metabolic and pre-biotic activities, the underlying transportation, and storage mechanisms of anthocyanins in rice are discussed in detail. This review provides potential information for the food industry and clues for rice breeding and genetic engineering of rice.

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