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Research Papers

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

[+] Author and Article Information
Tomasz Bartkowiak

Mem. ASME
Institute of Mechanical Technology,
Poznan University of Technology,
Pl. Marii Skłodowskiej-Curie 5,
Poznań 60-965, Poland
e-mail: tomasz.bartkowiak@put.poznan.pl

Christopher A. Brown

Surface Metrology Laboratory,
Worcester Polytechnic Institute,
100 Institute Road,
Worcester, MA 01609
e-mail: brown@wpi.edu

Manuscript received April 30, 2017; final manuscript received August 8, 2017; published online December 18, 2017. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 140(2), 021013 (Dec 18, 2017) (7 pages) Paper No: MANU-17-1292; doi: 10.1115/1.4037601 History: Received April 30, 2017; Revised August 08, 2017

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.

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Figures

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Fig. 1

Multiscale curvature tensor analysis: (a) curvature tensor calculation for nominal scale and (b) curvature tensor calculation for scale equal to two times the nominal sampling interval. The frame color corresponds to the color of the central point for which normal is estimated from 3 × 3 proximate points located within the frame. The central point is one of the three points in the triangular patch, the center of which is the location of the calculated curvature.

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Fig. 2

Renderings of measurements of surfaces created using different discharge energies

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Fig. 3

Maximum principal curvatures κ1 calculated at each position for surfaces created at different discharge energies (rows), calculated for two different scales of 1.875 μm (left column) and 3.75 μm (right column). The white plateaus represent the subareas for which values exceed the selected curvature scale which was selected to end at ±20 μm for all the energies to allow for direct comparisons between the different discharge energies.

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Fig. 4

Minimum principal curvature κ2 calculated at each position for surfaces created at different discharge energies (rows), calculated for two different scales of 1.875 μm (left column) and 3.75 μm (right column). Note that white plateaus represent the subareas for which values exceed the selected curvature scale which was selected to end at ±20 μm for all the energies to allow for comparisons between the different discharge energies.

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Fig. 5

Distributions of the actual values of the principal curvatures: (a) maximum magnitude, κ1 and (b) minimum magnitude κ2, computed at a scale of 1.250 μm for surfaces created with the indicated discharge energies. The sign indicates if the surface at a location and in that direction is concave (positive sign) or convex (negative). Note that scales are different on the plots depending on the discharge energy.

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Fig. 6

(a) Mean and (b) standard deviation of mean curvature H calculated at various scales

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Fig. 7

Coefficient of determination (R2) indicating the strengths of the correlations between discharge energies and statistical curvature parameters: (a) mean of maximum curvature κ1, (b) mean of minimum curvature κ2, (c) mean of mean curvature H, and (d) mean of Gaussian curvature K

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Fig. 8

Mean Gaussian curvature plus one standard deviation of Gaussian curvature, and discharge energy, calculated at scale of 3.125 μm: (a) linear regression and (b) exponential regression

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