Calculation of Surface Deformation in Point Contact EHD

1977 ◽  
Vol 99 (3) ◽  
pp. 313-317 ◽  
Author(s):  
S. Biswas ◽  
R. W. Snidle
Keyword(s):  
Surface Deformation ◽  
Point Contact ◽  
Order Method ◽  
Point Contacts ◽  
Numerical Techniques ◽  
Accurate Evaluation ◽  
First Order ◽  
Order Representation ◽  
Triangular Elements ◽  
Better Than

The paper describes three different numerical techniques for the accurate evaluation of the elastic deformation in elastohydrodynamic point contacts. The first method relies on a first order representation of the pressure distribution over triangular elements whereas the second and third methods use a second order method with rectangular elements. Comparison of results obtained using the numerical techniques described with known, exact values indicates that accuracies better than one percent can be expected when using the methods in the ehd problem.

In Support of Second Order Optimization

1991 ◽  
Author(s):  
Qiushi Cao ◽  
Prakash Krishnaswami
Keyword(s):  
Second Order ◽  
Optimization Techniques ◽  
Future Research ◽  
Order Method ◽  
First Order ◽  
Applied Optimization ◽  
Minimum Sensitivity ◽  
First Order Methods ◽  
Better Than ◽  
Second Order Methods

Abstract The vast majority of applied optimization falls into the category of first order optimization. This paper attempts to make the case for increased use of second order optimization techniques. Some of the most serious criticisms against second order methods are discussed and are shown to have lost some of their validity in recent years. In addition, some positive advantages of second order methods are also presented. These advantages include computational efficiency, compatibility with new advances in hardware and spill-over benefits in areas such as minimum sensitivity design. A simple second order constrained optimization algorithm is developed and several examples are solved using this method. A comparison is made with first order methods in terms of the number of function evaluations. The results show that the second order method performs much better than the first order methods in this regard. The paper also suggests some directions for future research in second order optimization.

scholarly journals Green–Haar wavelets method for generalized fractional differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mujeeb ur Rehman ◽  
Dumitru Baleanu ◽  
Jehad Alzabut ◽  
Muhammad Ismail ◽  
Umer Saeed
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Haar Wavelet ◽  
Haar Wavelets ◽  
Computational Time ◽  
Operational Matrices ◽  
Numerical Techniques ◽  
Fractional Differential ◽  
Fractional Boundary Value Problems ◽  
Better Than

Abstract The objective of this paper is to present two numerical techniques for solving generalized fractional differential equations. We develop Haar wavelets operational matrices to approximate the solution of generalized Caputo–Katugampola fractional differential equations. Moreover, we introduce Green–Haar approach for a family of generalized fractional boundary value problems and compare the method with the classical Haar wavelets technique. In the context of error analysis, an upper bound for error is established to show the convergence of the method. Results of numerical experiments have been documented in a tabular and graphical format to elaborate the accuracy and efficiency of addressed methods. Further, we conclude that accuracy-wise Green–Haar approach is better than the conventional Haar wavelets approach as it takes less computational time compared to the Haar wavelet method.

scholarly journals Electromigration-induced directional steps towards the formation of single atomic Ag contacts

2020 ◽  
Vol 11 ◽  
pp. 680-687
Author(s):  
Atasi Chatterjee ◽  
Christoph Tegenkamp ◽  
Herbert Pfnür
Keyword(s):  
Fourier Transforms ◽  
Single Point ◽  
Point Contact ◽  
Single Atom ◽  
Point Contacts ◽  
Cross Sectional ◽  
Shell Effects ◽  
Theoretical Approaches ◽  
Average Grain Size ◽  
Thinning Process

Even though there have been many experimental attempts and theoretical approaches to understand the process of electromigration (EM), it has not been quantitatively understood for ultrathin structures and at grain boundaries. Nevertheless, we showed recently that it can be used reliably for the formation of single atomic point contacts after careful pre-structuring of the initial Ag nanostructures. The process of formation of nanocontacts by EM down to a single-atom point contact was investigated for ultrathin (5 nm) Ag structures at 100 K by measuring the conductance as a function of the time during EM. In this paper, we compare the process of thinning by EM of structures with constrictions below the average grain size of Ag layers (15 nm) with that of structures with much larger initial constrictions of around 150 nm having multiple grains at the centre constriction prior to the formation of a point contact. Even though clear morphological differences exist between both types of structures, quantized conductance plateaus showing the formation of single point contacts have been observed for both. Here we put emphasis on the thinning process by EM, just before a point contact is formed. To understand this thinning process, the semi-classical regime before the contact reaches the quantum regime was analyzed in detail. For this purpose, we used experimental conductance histograms in the range between 2G 0 and 15G 0 and their corresponding Fourier transforms (FTs). The FT analysis of the conductance histograms exhibits a clear preference for thinning along the [100] direction. Using well-established models, both atom-by-atom steps and ranges of stability, presumably caused by electronic shell effects, can be discriminated. Although the directional motion of atoms during EM leads to specific properties such as the instabilities mentioned, similarities to mechanically opened contacts with respect to cross-sectional stability were found.

scholarly journals A thermal resistances-based approach for thermal-elastohydrodynamic calculations in point contacts

2017 ◽  
Vol 232 (11) ◽  
pp. 2088-2102 ◽  
Author(s):  
Eduardo de la Guerra Ochoa ◽  
Javier Echávarri Otero ◽  
Enrique Chacón Tanarro ◽  
Benito del Río López
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Thermal Effects ◽  
Good Accuracy ◽  
Computational Cost ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
New Approach ◽  
Ball On Disc

This article presents a thermal resistances-based approach for solving the thermal-elastohydrodynamic lubrication problem in point contact, taking the lubricant rheology into account. The friction coefficient in the contact is estimated, along with the distribution of both film thickness and temperature. A commercial tribometer is used in order to measure the friction coefficient at a ball-on-disc point contact lubricated with a polyalphaolefin base. These data and other experimental results available in the bibliography are compared to those obtained by using the proposed methodology, and thermal effects are analysed. The new approach shows good accuracy for predicting the friction coefficient and requires less computational cost than full thermal-elastohydrodynamic simulations.

scholarly journals Municipal Leachate Treatment by Fenton Process: Effect of Some Variable and Kinetics

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mohammad Ahmadian ◽  
Sohyla Reshadat ◽  
Nader Yousefi ◽  
Seyed Hamed Mirhossieni ◽  
Mohammad Reza Zare ◽  
...  
Keyword(s):  
Reaction Time ◽  
Color Removal ◽  
Molar Ratio ◽  
Order Kinetic ◽  
Fenton Process ◽  
Solution Ph ◽  
Leachate Treatment ◽  
First Order ◽  
Order Kinetic Model ◽  
Better Than

Due to complex composition of leachate, the comprehensive leachate treatment methods have been not demonstrated. Moreover, the improper management of leachate can lead to many environmental problems. The aim of this study was application of Fenton process for decreasing the major pollutants of landfill leachate on Kermanshah city. The leachate was collected from Kermanshah landfill site and treated by Fenton process. The effect of various parameters including solution pH, Fe2+and H2O2dosage, Fe2+/H2O2molar ratio, and reaction time was investigated. The result showed that with increasing Fe2+and H2O2dosage, Fe2+/H2O2molar ratio, and reaction time, the COD, TOC, TSS, and color removal increased. The maximum COD, TOC, TSS, and color removal were obtained at low pH (pH: 3). The kinetic data were analyzed in term of zero-order, first-order, and second-order expressions. First-order kinetic model described the removal of COD, TOC, TSS, and color from leachate better than two other kinetic models. In spite of extremely difficulty of leachate treatment, the previous results seem rather encouraging on the application of Fenton’s oxidation.

scholarly journals Point contact spectroscopy of superconductors via nanometer scale point contacts formed by resistive switching

AIP Advances ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 125217 ◽  
Author(s):  
Mária Dvoranová ◽  
Tomáš Plecenik ◽  
Martin Moško ◽  
Marek Vidiš ◽  
Maroš Gregor ◽  
...  
Keyword(s):  
Resistive Switching ◽  
Point Contact ◽  
Nanometer Scale ◽  
Point Contacts ◽  
Point Contact Spectroscopy ◽  
Scale Point

scholarly journals The Effects of Artificially-Produced Defects on the Film Thickness Distribution in Sliding EHD Point Contacts

1982 ◽  
Vol 104 (3) ◽  
pp. 365-375 ◽  
Author(s):  
C. Cusano ◽  
L. D. Wedeven
Keyword(s):  
Film Thickness ◽  
Contact Region ◽  
Thickness Distribution ◽  
Point Contact ◽  
Optical Interferometry ◽  
Point Contacts ◽  
Thickness Profile ◽  
Inlet Region

The effects of artificially-produced dents and grooves on the elastohydrodynamic (EHD) film thickness profile in a sliding point contact are investigated by means of optical interferometry. The defects, formed on the surface of a highly polished ball, are held stationary at various locations within and in the vicinity of the contact region while the disk is rotating. It is shown that the defects, having a geometry similar to what can be expected in practice, can dramatically change the film thickness which exists when no defects are present in or near the contact. This change in film thickness is mainly a function of the position of the defects in the inlet region, the geometry of the defects, the orientation of the defects in the case of grooves, and the depth of the defect relative to the central film thickness.

scholarly journals Lubrication Analyses of Cam and Flat-Faced Follower

Lubricants ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 31 ◽  
Author(s):  
Hazim U. Jamali ◽  
Amjad Al-Hamood ◽  
Oday I. Abdullah ◽  
Adolfo Senatore ◽  
Josef Schlattmann
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Surface Deformation ◽  
Numerical Study ◽  
Point Contact ◽  
Radius Of Curvature ◽  
Operating Cycle ◽  
Essential Step ◽  
Parabolic Shape ◽  
Principal Factors

The principal factors that affect the characteristics of contact problem between cam and follower vary enormously during the operating cycle of this mechanism. This includes radius of curvature, surface velocities and applied load. It has been found over the last decades that the mechanism operates under an extremely thin film of lubricant. Any practical improvement in the level of film thickness that separates the contacted surfaces represents an essential step towards a satisfactory design of the system. In this paper a detailed numerical study is presented for the cam and follower (flat-faced) lubrication including the effect of introducing an axial modification (parabolic shape) of the cam depth on the levels of film thickness and pressure distribution. This is achieved based on a point contact model for a cam and flat-faced follower system. The results reveal that the cam form of modification has considerable consequences on the level of predicted film thickness and pressure distribution as well as surface deformation.

Higher-Order Multilevel Solvers for the EHL Line and Point Contact Problem

1994 ◽  
Vol 116 (4) ◽  
pp. 741-750 ◽  
Author(s):  
C. H. Venner
Keyword(s):  
Contact Problem ◽  
Computing Time ◽  
Point Contact ◽  
Higher Order ◽  
Second Order ◽  
Point Of View ◽  
First Order ◽  
Fundamental Point ◽  
Numerical Solver ◽  
Circular Contact

This paper addresses the development of efficient numerical solvers for EHL problems from a rather fundamental point of view. A work-accuracy exchange criterion is derived, that can be interpreted as setting a limit to the price paid in terms of computing time for a solution of a given accuracy. The criterion can serve as a guideline when reviewing or selecting a numerical solver and a discretization. Earlier developed multilevel solvers for the EHL line and circular contact problem are tested against this criterion. This test shows that, to satisfy the criterion a second-order accurate solver is needed for the point contact problem whereas the solver developed earlier used a first-order discretization. This situation arises more often in numerical analysis, i.e., a higher order discretization is desired when a lower order solver already exists. It is explained how in such a case the multigrid methodology provides an easy and straightforward way to obtain the desired higher order of approximation. This higher order is obtained at almost negligible extra work and without loss of stability. The approach was tested out by raising an existing first order multilevel solver for the EHL line contact problem to second order. Subsequently, it was used to obtain a second-order solver for the EHL circular contact problem. Results for both the line and circular contact problem are presented.

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