Characterization of 3D Surface Texture Directionality Using Multi-Scale Curvature Tensor Analysis

2017 ◽  
Author(s):  
Tomasz Bartkowiak
Keyword(s):  
Curvature Tensor ◽  
Surface Texture ◽  
Sampling Interval ◽  
Tensor Analysis ◽  
Principal Curvatures ◽  
Multi Scale ◽  
Principal Directions ◽  
2D And 3D ◽  
3D Surface Texture

Anisotropy of surface texture can in many practical cases significantly affect the interaction between the surface and phenomena that influence or are influenced by the topography. Tribological contacts in sheet forming, wetting behavior or dental wear are good examples. This article introduces and exemplifies a method for quantification and visualization of anisotropy using the newly developed 3D multi-scale curvature tensor analysis. Examples of a milled steel surface, which exhibited an evident anisotropy, and a ruby contact probe surface, which was the example of isotropic surface, were measured by the confocal microscope. They were presented in the paper to support the proposed approach. In the method, the curvature tensor T is calculated using three proximate unit vectors normal to the surface. The multi-scale effect is achieved by changing the size of the sampling interval for the estimation of the normals. Normals are estimated from regular meshes by applying a covariance matrix method. Estimation of curvature tensor allows determination of two directions around which surface bends the most and the least (principal directions) and the bending radii (principal curvatures). The direction of the normal plane, where the curvature took its maximum, could be plotted for each analyzed region and scale. In addition, 2D and 3D distribution graphs could be provided to visualize anisotropic or isotropic characteristics. This helps to determine the dominant texture direction or directions for each scale. In contrast to commonly used surface isotropy/anisotropy determination techniques such as Fourier transform or autocorrelation, the presented method provides the analysis in 3D and for every region at each scale. Thus, different aspects of the studied surfaces could clearly be seen at different scales.

scholarly journals Analysis of Surface Microgeometry Created by Electric Discharge Machining

Materials ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 3830
Author(s):  
Tomasz Bartkowiak ◽  
Michał Mendak ◽  
Krzysztof Mrozek ◽  
Michał Wieczorowski
Keyword(s):  
Curvature Tensor ◽  
Electric Discharge ◽  
Surface Characterization ◽  
Tensor Analysis ◽  
Principal Curvatures ◽  
Motif Analysis ◽  
Electric Discharge Machining ◽  
Surface Microgeometry ◽  
Focus Variation

The objective of this work is to study the geometric properties of surface topographies of hot-work tool steel created by electric discharge machining (EDM) using motif and multiscale analysis. The richness of these analyses is tested through calculating the strengths of the correlations between discharge energies and resulting surface characterization parameters, focusing on the most representative surface features—craters, and how they change with scale. Surfaces were created by EDM using estimated energies from 150 to 9468 µJ and measured by focus variation microscope. The measured topographies consist of overlapping microcraters, of which the geometry was characterized using three different analysis: conventional with ISO parameters, and motif and multiscale curvature tensor analysis. Motif analysis uses watershed segmentation which allows extraction and geometrically characterization of each crater. Curvature tensor analysis focuses on the characterization of principal curvatures and their function and their evolution with scale. Strong correlations (R2 > 0.9) were observed between craters height, diameter, area and curvature using linear and logarithmic regressions. Conventional areal parameter related to heights dispersion were found to correlate stronger using logarithmic regression. Geometric characterization of process-specific topographic formations is considered to be a natural and intuitive way of analyzing the complexity of studied surfaces. The presented approach allows extraction of information directly relating to the shape and size of topographic features of interest. In the tested conditions, the surface finish is mostly affected and potentially controlled by discharge energy at larger scales which is associated with sizes of fabricated craters.

On the Invariance of Gear Tooth Curvature

2006 ◽  
Vol 220 (7) ◽  
pp. 1083-1096 ◽  
Author(s):  
D B Dooner
Keyword(s):  
Gear Tooth ◽  
Helix Angle ◽  
Gear Pair ◽  
Principal Curvatures ◽  
Gear Teeth ◽  
Conical Gears ◽  
Tooth Type ◽  
Instantaneous Pressure ◽  
Principal Directions

A method is presented for the determination of the principal curvatures along with their principal directions of two gear teeth in direct contact. The procedure used to determine these extreme curvatures and directions is based on the nominal position of contact. Moreover, these extreme curvatures and directions are invariant with tooth type (viz. involute and cycloidal) and manufacturing process. Such curvatures and directions depend on the instantaneous pressure angle, spiral or helix angle, and position of contact. This generalized method is applicable to cylindrical gears (spur and helical), conical gears (straight and spiral), as well as hyperboloidal gears (hypoid and worm). Three examples are included to illustrate the determination of principal curvatures and directions. The first example is a helical gear pair, the second is a spiral bevel gear pair, and the third example is a hypoid gear pair.

A Characterization of Process–Surface Texture Interactions in Micro-Electrical Discharge Machining Using Multiscale Curvature Tensor Analysis

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Tomasz Bartkowiak ◽  
Christopher A. Brown
Keyword(s):  
Curvature Tensor ◽  
Electrical Discharge ◽  
Electrical Discharge Machining ◽  
Sampling Interval ◽  
Tensor Analysis ◽  
Strong Correlations ◽  
Micro Electrical Discharge Machining ◽  
Surface Topographies ◽  
Unit Vectors

The objectives of this work are to demonstrate the use of multiscale curvature tensor analysis for characterizing surfaces of stainless steel created by micro-electrical discharge machining (μEDM), and to study the strengths of the correlations between discharge energies and resulting surface curvatures (i.e., principal, Gaussian, or mean curvatures) and how they change with scale. Surfaces were created by μEDM techniques using energies from 18 nJ to 16,500 nJ and measured by confocal microscope. The curvature tensor T is calculated using three proximate unit vectors normal to the surface. The multiscale effect is achieved by changing the size of the sampling interval for the estimation of the normals. Normals are estimated from regular meshes by applying a covariance matrix method. Strong correlations (R2 > 0.9) are observed between calculated principal maximal and minimal as well as mean and Gaussian curvatures and discharge energies. This method allows detailed analysis of the nature of surface topographies and suggests that different formation processes governed the creation of surfaces created by higher energies.

2D and 3D Surface Texture Comparisons Using Autocorrelation Functions

2005 ◽  
Vol 295-296 ◽  
pp. 437-440 ◽  
Author(s):  
J. Song ◽  
L. Ma ◽  
E. Whitenton ◽  
T. Vorburger
Keyword(s):  
Measurement System ◽  
Surface Texture ◽  
Cross Correlation ◽  
Maximum Correlation ◽  
Surface Textures ◽  
Difference Function ◽  
3D Surface ◽  
The Difference ◽  
2D And 3D ◽  
3D Surface Texture

Autocorrelation and cross-correlation functions are proposed for 2D and 3D surface texture comparisons. At the maximum correlation point of the two correlated surface textures, there is a peak shown at the cross-correlation curve. It is proposed to generate a difference function at the maximum correlation point for evaluation of the difference between the two compared surface textures. Based on this method, the National Institute of Standards and Technology (NIST) bullet signature measurement system is developed for the bullet signature measurements of NIST standard bullets.

scholarly journals A parametric prediction of the Young’s modulus of polymers enhanced with ΜWCNTs

2018 ◽  
Vol 233 ◽  
pp. 00025
Author(s):  
P.V. Polydoropoulou ◽  
K.I. Tserpes ◽  
Sp.G. Pantelakis ◽  
Ch.V. Katsiropoulos
Keyword(s):  
Young’S Modulus ◽  
Elastic Properties ◽  
Young's Modulus ◽  
Experimental Results ◽  
Scale Model ◽  
Fe Model ◽  
Multi Scale ◽  
Unit Cells ◽  
Random Dispersion

In this work a multi-scale model simulating the effect of the dispersion, the waviness as well as the agglomerations of MWCNTs on the Young’s modulus of a polymer enhanced with 0.4% MWCNTs (v/v) has been developed. Representative Unit Cells (RUCs) have been employed for the determination of the homogenized elastic properties of the MWCNT/polymer. The elastic properties computed by the RUCs were assigned to the Finite Element (FE) model of a tension specimen which was used to predict the Young’s modulus of the enhanced material. Furthermore, a comparison with experimental results obtained by tensile testing according to ASTM 638 has been made. The results show a remarkable decrease of the Young’s modulus for the polymer enhanced with aligned MWCNTs due to the increase of the CNT agglomerations. On the other hand, slight differences on the Young’s modulus have been observed for the material enhanced with randomly-oriented MWCNTs by the increase of the MWCNTs agglomerations, which might be attributed to the low concentration of the MWCNTs into the polymer. Moreover, the increase of the MWCNTs waviness led to a significant decrease of the Young’s modulus of the polymer enhanced with aligned MWCNTs. The experimental results in terms of the Young’s modulus are predicted well by assuming a random dispersion of MWCNTs into the polymer.

Estimation of Service Life of Mechanical Engineering Components

2019 ◽  
Vol 799 ◽  
pp. 71-76
Author(s):  
Oskars Linins ◽  
Ernests Jansons ◽  
Armands Leitans ◽  
Irina Boiko ◽  
Janis Lungevics
Keyword(s):  
Service Life ◽  
Service Time ◽  
Surface Texture ◽  
Mechanical Engineering ◽  
Friction Pair ◽  
Theory Of Elasticity ◽  
New Approach ◽  
Material Fatigue ◽  
Texture Parameters ◽  
3D Surface Texture

The paper is aimed to the methodology for estimation of service life of mechanical engineering components in the case of elastic-plastic contact of surfaces. Well-known calculation methods depending on physics, theory of probability, the analysis of friction pair’ shape and fit include a number of parameters that are difficult or even impossible to be technologically controlled in the manufacturing of mechanical engineering components. The new approach for wear rate estimation using surface texture parameters as well as physical-mechanical properties and geometric parameters of components is proposed. The theoretical part of the calculations is based on the 3D surface texture principles, the basics of material fatigue theory, the theory of elasticity and the contact mechanics of surfaces. It is possible to calculate the service time of the machine, but the process of running-in of the components is relatively short (less than 5%), therefore, the service time is mainly determined by a normal operating period, which also was used to evaluate this period. The calculated input parameters are technologically and metrologically available and new method for calculating the service time can be used in the design process of the equipment. The results of approbation of the method for estimation service time of mechanical engineering, which prove the applicability of mentioned method, are offered as well.

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