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Journal ArticleDOI

A versatile method of discrete convolution and FFT (DC-FFT) for contact analyses

28 Aug 2000-Wear (Elsevier)-Vol. 243, Iss: 1, pp 101-111
TL;DR: In this article, Discrete convolution and FFT (DC-FFT) is adopted instead of the method of continuous convolutions and Fourier transform for the contact problems.
About: This article is published in Wear.The article was published on 2000-08-28. It has received 613 citations till now. The article focuses on the topics: Split-radix FFT algorithm & Prime-factor FFT algorithm.
Citations
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Journal ArticleDOI
TL;DR: In this article, the DC-FFT algorithm was used to analyze the contact stresses in an elastic body under pressure and shear tractions for high efficiency and accuracy, and a set of general formulas of the frequency response function for the elastic field was derived and verified.
Abstract: The knowledge of contact stresses is critical to the design of a tribological element. It is necessary to keep improving contact models and develop efficient numerical methods for contact studies, particularly for the analysis involving coated bodies with rough surfaces. The fast Fourier Transform technique is likely to play an important role in contact analyses. It has been shown that the accuracy in an algorithm with the fast Fourier Transform is closely related to the convolution theorem employed. The algorithm of the discrete convolution and fast Fourier Transform, named the DC-FFT algorithm includes two routes of problem solving: DC-FFT/Influence coefficients/Green's, function for the cases with known Green's functions and DC-FFT/Influence coefficient/conversion, if frequency response functions are known. This paper explores the method for the accurate conversion for influence coefficients from frequency response functions, further improves the DC- FFT algorithm, and applies this algorithm to analyze the contact stresses in an elastic body under pressure and shear tractions for high efficiency and accuracy. A set of general formulas of the frequency response function for the elastic field is derived and verified. Application examples are presented and discussed.

265 citations

Journal ArticleDOI
TL;DR: In this article, the effects of texture bottom shape and surface relative motion on lubrication enhancement using numerically generated textures by means of model-based virtual texturing and numerical simulation were investigated.
Abstract: The geometry of micro-scale textures and the relative motion of surfaces in contact may affect the performance of an elastohydrodynamic lubrication interface. Reported in this paper are the investigations of the effects of texture bottom shape and surface relative motion on lubrication enhancement using numerically generated textures by means of model-based virtual texturing and numerical simulation. These textures are on one of the interacting surfaces in a triangular distribution and have the same density. The results suggest that the bottom shapes involving a micro-wedge and/or a micro-step bearing tend to yield thicker films. The lubrication of selected textured surfaces was also studied under three different relative motions: texture surface moving, un-textured surface moving, and both moving. The results indicate that textures on the faster moving surface offer stronger film thickness enhancement.

195 citations

Journal ArticleDOI
TL;DR: In this paper, the authors discussed the tribological mechanisms, scale effects and surface parameters influencing the friction and wear of diamond and DLC-coated surfaces and showed how surface 3D FEM modelling generates stress and strain values at the nano level, within bond layers at coating/substrate interfaces and around cracks and forms the basis for better understanding the origin of wear.
Abstract: Coating a surface with a thin layer changes the surface material properties and is an important tool for controlling friction and wear. The tribological mechanisms, scale effects and parameters influencing the friction and wear of coated surfaces are discussed. The basic friction and wear mechanisms can be reduced to: friction by adhesion, ploughing and hysteresis and wear by adhesion, abrasion and fatigue combined with material fracture. The tribochemical and surface physical effects and surface fatigue taking place before material fracture are treated here as pure surface material modification mechanisms. Scale effects in a tribological contact are illustrated by explaining typical surface roughness related tribological mechanisms for diamond and DLC coated surfaces. For diamond coatings asperity interlocking effects are important for rough surfaces, graphitisation is a dominating mechanism for smooth engineering surfaces and hydrogenising of dangling bonds may be crucial for physically smooth surfaces. For DLC coated surfaces, surface graphitisation is important with rougher surfaces; building up transfer layers and graphitisation is crucial for smooth engineering surfaces and hydrogenising of dangling bonds can explain superlubricity for physically smooth surfaces. An analysis of dominating surface parameters such as elastic, plastic and fracture behaviour of the top surface, the coating, the coating/substrate interface and the substrate in addition to the coating thickness forms the basis for surface modelling. A stress intensity factor analysis of crack growth shows the importance of considering both modes I, II and III loading, crack spacing and location of crack, while crack orientation, location in crack field as well as load biaxiality have minor influences. It is shown how surface 3D FEM modelling generates stress and strain values at the nano level, within bond layers at coating/substrate interfaces and around cracks and forms the basis for better understanding the origin of wear.

181 citations

Journal ArticleDOI
01 Apr 2010
TL;DR: A mixed lubrication model that permits real 3D surface topography as input is developed in this paper, and the theory of computing flow factors within the model is presented, and with a follow-up paper.
Abstract: A mixed lubrication model that permits real three-dimensional surface topography as input is developed. The theory of computing flow factors within the model is presented, and with a follow...

135 citations

Journal ArticleDOI
TL;DR: In this article, an analytical numerical model was developed to understand the tribological behavior of textured surfaces in mixed lubrication regime, which employed the average flow Reynolds equation and an elasto-plastic contact model, established on the basis of finite element analysis, to calculate the hydrodynamic pressure in full film region and the contact pressure in contact region, respectively.

122 citations

References
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MonographDOI
01 Jan 1985

5,957 citations

Book
01 Jan 1965
TL;DR: In this paper, the authors provide a broad overview of Fourier Transform and its relation with the FFT and the Hartley Transform, as well as the Laplace Transform and the Laplacian Transform.
Abstract: 1 Introduction 2 Groundwork 3 Convolution 4 Notation for Some Useful Functions 5 The Impulse Symbol 6 The Basic Theorems 7 Obtaining Transforms 8 The Two Domains 9 Waveforms, Spectra, Filters and Linearity 10 Sampling and Series 11 The Discrete Fourier Transform and the FFT 12 The Discrete Hartley Transform 13 Relatives of the Fourier Transform 14 The Laplace Transform 15 Antennas and Optics 16 Applications in Statistics 17 Random Waveforms and Noise 18 Heat Conduction and Diffusion 19 Dynamic Power Spectra 20 Tables of sinc x, sinc2x, and exp(-71x2) 21 Solutions to Selected Problems 22 Pictorial Dictionary of Fourier Transforms 23 The Life of Joseph Fourier

5,714 citations

Journal ArticleDOI

1,534 citations


"A versatile method of discrete conv..." refers background in this paper

  • ...or cyclic sense identically means that one should add this NH(r−j) term to the subscript, and in a computation process, the termNH(r−j) must be rigidly required [9,10]....

    [...]

Book
08 Apr 1988

1,453 citations

Book
01 Jul 1988
TL;DR: This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.
Abstract: The Fast Fourier Transform (FFT) is a mathematical method widely used in signal processing. This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.

1,432 citations


"A versatile method of discrete conv..." refers background in this paper

  • ...or cyclic sense identically means that one should add this NH(r−j) term to the subscript, and in a computation process, the termNH(r−j) must be rigidly required [9,10]....

    [...]