Combining and Contacting of Two Rough Surfaces with Asymmetric Distribution of Asperity Heights

2004 ◽  
Vol 126 (2) ◽  
pp. 225-232 ◽  
Author(s):  
Ning Yu ◽  
Andreas A. Polycarpou
Keyword(s):  
Standard Deviation ◽  
Weibull Distribution ◽  
Rough Surface ◽  
Rough Surfaces ◽  
Asymmetric Distribution ◽  
Magnetic Storage ◽  
Roughness Parameters ◽  
Practical Applications ◽  
Practical Engineering ◽  
Contour Plots

The statistical approach of describing rough surfaces is extended to include the contact of two rough surfaces in which their distribution of asperity heights can either be symmetric or asymmetric, and the asymmetry is modeled using the normalized Weibull distribution. In considering the contact between two rough surfaces, as in most practical applications, the contact can be approximated by an equivalent rough surface in contact with a smooth plane. The roughness parameters of the equivalent surface are obtained using the spectral moment method, and its validity is verified using realistic surface roughness measurements. This paper presents a method to obtain the equivalent rough surface with a Weibull distribution of asperity heights, in which the standard deviation and skewness parameters of asperity heights of the actual contacting surfaces are preserved. The advantages of this method are demonstrated via direct comparisons with a previously proposed method as well as with exact numerical simulation of the contact parameters of several different actual surfaces from magnetic storage and MEMS applications. For practical engineering applications, where the roughness parameters of each individual surface are known, contour plots for the skewness value of the equivalent rough surface are provided for practical ranges of combinations of standard deviation ratios and skewness values. As expected when the roughness of one of the contacting surfaces dominates, the skewness is solely determined by the rougher surface.

Topography Analysis of Random Anisotropic Gaussian Rough Surfaces

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Deepak K. Prajapati ◽  
Mayank Tiwari
Keyword(s):  
Standard Deviation ◽  
Rough Surface ◽  
Correlation Length ◽  
Rough Surfaces ◽  
Spectral Moments ◽  
Statistical Characterization ◽  
Wear Process ◽  
Increase With Increase ◽  
Bandwidth Parameter ◽  
Significant Difference

Engineered surfaces (ground and similarly structured rough surfaces) show anisotropic characteristics and their topography parameters are direction dependent. Statistical characterization of these surfaces is still complex because of directional nature of surfaces. In this technical brief, an attempt is made to simulate anisotropic surfaces through use of topography parameters (three-dimensional (3D) surface parameters). First, 3D anisotropic random Gaussian rough surface is generated numerically with fast Fourier transform (FFT). Numerically generated anisotropic random Gaussian rough surface shows statistical properties (texture direction, texture ratio) similar to ground and similarly directional anisotropic rough surfaces. For numerically generated anisotropic Gaussian rough surface, important 3D roughness parameters are determined. Sayles and Thomas' (1976, “Thermal Conductance of Rough Elastic Contact,” Appl. Energy, 2(4), pp. 249–267.) theoretical model for directional anisotropic rough surface is adopted here for calculating the summit parameters, i.e., equivalent bandwidth parameter, mean summit curvature, skewness of summit height, standard deviation of summit height, and equivalent spectral moments. This work demonstrates the variation of spectral moments in both across and parallel to the lay directions with pattern ratio (γ=βx/βy). Correlation length (βx) is fixed 10μm and correlation length (βy) is varied from 100 to 10 μm. Variation of summit parameters with pattern ratio is also discussed in detail. Results shows that mean summit curvature and skewness of summit heights increase with increase in pattern ratio, whereas standard deviation of summit heights and equivalent bandwidth parameter (αe) decreases with pattern ratio. A significant difference is found in “Abbott-Firestone” parameters when calculated in both perpendicular and parallel to lay directions. Effect of these parameters on wear process is discussed in brief.

Contact of Rough Surfaces With Asymmetric Distribution of Asperity Heights

2001 ◽  
Vol 124 (2) ◽  
pp. 367-376 ◽  
Author(s):  
Ning Yu ◽  
Andreas A. Polycarpou
Keyword(s):  
Weibull Distribution ◽  
Rough Surfaces ◽  
Closed Form Solution ◽  
Form Solution ◽  
Asymmetric Distribution ◽  
Exponential Distributions ◽  
Real Area Of Contact ◽  
Gaussian Case ◽  
Different Levels ◽  
Key Parameter

The Greenwood and Williamson (GW) statistical approach of characterizing rough surfaces is extended to include asymmetric distribution of asperity heights using the Weibull distribution. A key parameter that is used to characterize asymmetry is the skewness, and the corresponding Weibull parameters are investigated for a range of practical skewness values. The Weibull distribution is then adopted to model the asperity heights, and once normalized, is used to calculate the contact load, real area of contact and number of contacting asperities using the CEB elastic-plastic model of an equivalent rough surface in contact with a smooth plane. The effect of skewness on different levels of surface roughness, ranging from very smooth surfaces encountered in microtribological applications to rougher surfaces encountered in macrotribological applications is investigated, and also compared to the symmetric Gaussian case. Also, to allow for closed-form solution of the contact equations, simpler exponential distributions are curved-fitted to the contact side of the Weibull distribution, and the analytical results are favorably compared with the numerical results using the Weibull distribution.

scholarly journals Rectangle-capped and tilted micropillar array for enhanced anisotropic anti-shearing in biomimetic adhesion

2015 ◽  
Vol 12 (106) ◽  
pp. 20150090 ◽  
Author(s):  
Yue Wang ◽  
Xiangming Li ◽  
Hongmiao Tian ◽  
Hong Hu ◽  
Yu Tian ◽  
...  
Keyword(s):  
Rough Surfaces ◽  
Moulding Process ◽  
Practical Applications ◽  
Dry Adhesion ◽  
Dry Adhesives ◽  
Shearing Strength ◽  
Self Cleaning ◽  
Reverse Shearing ◽  
Orthogonal Anisotropy ◽  
Micropillar Array

Dry adhesion observed in the feet of various small creatures has attracted considerable attention owing to the unique advantages such as self-cleaning, adaptability to rough surfaces along with repeatable and reversible adhesiveness. Among these advantages, for practical applications, proper detachability is critical for dry adhesives with artificial microstructures. In this study, we present a microstructured array consisting of both asymmetric rectangle-capped tip and tilted shafts, which produce an orthogonal anisotropy of the shearing strength along the long and short dimensions of the tip, with a maximum anti-shearing in the two directions along the longer dimension. Meanwhile, the tilt feature can enhance anisotropic shearing adhesion by increasing shearing strength in the forward shearing direction and decreasing strength in the reverse shearing direction along the short dimension of the tip, leading to a minimum anti-shearing in only one of the two directions along the shorter dimension of the rectangular tip. Such a microstructured adhesive with only one weak shearing direction, leading to well-controlled attachment and detachment of the adhesive, is created in our experiment by conventional double-sided exposure of a photoresist followed by a moulding process.

Reduced Rough-Surface Parametrization for Use With the Discrete-Element Model

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Stephen T. McClain ◽  
Jason M. Brown
Keyword(s):  
Heat Transfer ◽  
Rough Surface ◽  
Surface Characterization ◽  
Rough Surfaces ◽  
Roughness Element ◽  
Three Dimensional ◽  
Element Model ◽  
Discrete Element ◽  
Diameter Distribution ◽  
Discrete Element Model

The discrete-element model for flows over rough surfaces was recently modified to predict drag and heat transfer for flow over randomly rough surfaces. However, the current form of the discrete-element model requires a blockage fraction and a roughness-element diameter distribution as a function of height to predict the drag and heat transfer of flow over a randomly rough surface. The requirement for a roughness-element diameter distribution at each height from the reference elevation has hindered the usefulness of the discrete-element model and inhibited its incorporation into a computational fluid dynamics (CFD) solver. To incorporate the discrete-element model into a CFD solver and to enable the discrete-element model to become a more useful engineering tool, the randomly rough surface characterization must be simplified. Methods for determining characteristic diameters for drag and heat transfer using complete three-dimensional surface measurements are presented. Drag and heat transfer predictions made using the model simplifications are compared to predictions made using the complete surface characterization and to experimental measurements for two randomly rough surfaces. Methods to use statistical surface information, as opposed to the complete three-dimensional surface measurements, to evaluate the characteristic dimensions of the roughness are also explored.

scholarly journals Comparison Of Three Numerical Methods For Estimating Weibull Parameters Using Weibull Distribution Model In Nigeria

2020 ◽  
Vol 27 (2) ◽  
pp. 8-15
Author(s):  
J.A. Oyewole ◽  
F.O. Aweda ◽  
D. Oni
Keyword(s):  
Standard Deviation ◽  
Wind Speed ◽  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Accurate Estimation ◽  
Weibull Parameters ◽  
Factor Method ◽  
Deviation Method

There is a crucial need in Nigeria to enhance the development of wind technology in order to boost our energy supply. Adequate knowledge about the wind speed distribution becomes very essential in the establishment of Wind Energy Conversion Systems (WECS). Weibull Probability Density Function (PDF) with two parameters is widely accepted and is commonly used for modelling, characterizing and predicting wind resource and wind power, as well as assessing optimum performance of WECS. Therefore, it is paramount to precisely estimate the scale and shape parameters for all regions or sites of interest. Here, wind data from year 2000 to 2010 for four different locations (Port Harcourt, Ikeja, Kano and Jos) were analysed and the Weibull parameters was determined. The three methods employed are Mean Standard Deviation Method (MSDM), Energy Pattern Factor Method (EPFM) and Method of Moments (MOM) for estimating Weibull parameters. The method that gave the most accurate estimation of the wind speed was MSDM method, while Energy Pattern Factor Method (EPFM) is the most reliable and consistent method for estimating probability density function of wind. Keywords: Weibull Distribution, Method of Moment, Mean Standard Deviation Method, Energy Pattern Method

Reduced Rough-Surface Parameterization for Use With the Discrete-Element Model

2007 ◽  
Author(s):  
Stephen T. McClain ◽  
Jason M. Brown
Keyword(s):  
Heat Transfer ◽  
Rough Surface ◽  
Surface Characterization ◽  
Rough Surfaces ◽  
Roughness Element ◽  
Three Dimensional ◽  
Element Model ◽  
Discrete Element ◽  
Diameter Distribution ◽  
Discrete Element Model

The discrete-element model for flows over rough surfaces was recently modified to predict drag and heat transfer for flow over randomly-rough surfaces. However, the current form of the discrete-element model requires a blockage fraction and a roughness-element diameter distribution as a function of height to predict the drag and heat transfer of flow over a randomly-rough surface. The requirement for a roughness element-diameter distribution at each height from the reference elevation has hindered the usefulness of the discrete-element model and inhibited its incorporation into a computational fluid dynamics (CFD) solver. To incorporate the discrete-element model into a CFD solver and to enable the discrete-element model to become a more useful engineering tool, the randomly-rough surface characterization must be simplified. Methods for determining characteristic diameters for drag and heat transfer using complete three-dimensional surface measurements are presented. Drag and heat transfer predictions made using the model simplifications are compared to predictions made using the complete surface characterization and to experimental measurements for two randomly-rough surfaces. Methods to use statistical surface information, as opposed to the complete three-dimensional surface measurements, to evaluate the characteristic dimensions of the roughness are also explored.

scholarly journals A New Flexible Bathtub-Shaped Modification of the Weibull Model: Properties and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Qinghu Liao ◽  
Zubair Ahmad ◽  
Eisa Mahmoudi ◽  
G. G. Hamedani
Keyword(s):  
Weibull Distribution ◽  
Hazard Rate ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Weibull Model ◽  
Rate Function ◽  
Model Parameters ◽  
Hazard Functions ◽  
Practical Applications ◽  
Nonnested Models

Many studies have suggested the modifications and generalizations of the Weibull distribution to model the nonmonotone hazards. In this paper, we combine the logarithms of two cumulative hazard rate functions and propose a new modified form of the Weibull distribution. The newly proposed distribution may be called a new flexible extended Weibull distribution. Corresponding hazard rate function of the proposed distribution shows flexible (monotone and nonmonotone) shapes. Three different characterizations along with some mathematical properties are provided. We also consider the maximum likelihood estimation procedure to estimate the model parameters. For the illustrative purposes, two real applications from reliability engineering with bathtub-shaped hazard functions are analyzed. The practical applications show that the proposed model provides better fits than the other nonnested models.

UV Nano-Imprint Lithography for Manufacturing Applications

2007 ◽  
Author(s):  
Jin Choi ◽  
S. V. Sreenivasan ◽  
Doug Resnick
Keyword(s):  
Uv Curing ◽  
Magnetic Storage ◽  
Imprint Lithography ◽  
Practical Applications ◽  
Drop On Demand ◽  
Defect Repair ◽  
Manufacturing Applications ◽  
Near Term ◽  
Layer Control ◽  
Nano Imprint

Researchers have demonstrated that imprint lithography techniques have remarkable replication resolution and can pattern sub-5nm structures. However, a fully capable lithography approach needs to address several challenges in order to be useful in nano-manufacturing applications. This paper presents the key technical challenges as well as the progress achieved to-date in these areas. A promising nanoimprint technique that has been previously discussed in the literature is a UV curing technique known as Step and Flash Imprint Lithography (S-FIL). In this article, a variant of the S-FIL process — known as drop-on-demand UV nano-imprint process — that addresses many of the key manufacturing challenges is discussed. This process has the ability to address challenges such as process repeatability in residual layer control, low defectivity, ability to fully automate the lithography process, nano-resolution alignment, and the ability to handle pattern density variations. All nano-imprint lithography techniques essentially replicate the patterns present in a master mold (or template). One of the demanding challenges is the creation of this template. Patterning, metrology, inspection, and defect repair issues relevant to template fabrication are discussed. Finally, with a brief discussion of near-term practical applications in the areas of photonics, magnetic storage, and CMOS devices is presented.

Modeling of rough surfaces with given roughness parameters

2017 ◽  
Vol 24 (1) ◽  
pp. 127-136 ◽  
Author(s):  
Wei Zhou ◽  
Jin-yuan Tang ◽  
Yan-fei He ◽  
Cai-chao Zhu
Keyword(s):  
Rough Surfaces ◽  
Roughness Parameters
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