Two basic components make up the value added to a work piece by the micro-electric discharge machining (μEDM) process: form and surface finish. Understanding the correlations between processing parameters and surface finish (topography) is important for the improvement of process design and process control. The relation between process variables and surface topography can be used to improve both process design and control, helping better control the performance of a product by controlling μEDM parameters.

In order to examine the relation between μEDM and the surface topography of stainless steel, a stainless-steel surface can be measured using a laser scanning confocal microscope. These measurements can then be characterized with conventional parameters as well as parameters from multi-scale areal fractal analysis.


The objective of this study was to investigate the relationship between the energy for μEDM of stainless steel and the resulting surface topography, in particular the correlations between topographic characterizations (ASME B46.1) and machining energy. This work also examined the application of laser scanning confocal microscopy for the measurement and graphic representation of surfaces formed by μEDM and addressed the importance of scale in surface measurement and characterization.


A laser scanning confocal microscope (Olympus LEXT OLS4000) was used to measure the topographies of surfaces created by μEDM (surfaces machined by SmalTec GM703) with different discharge energies. These measurements were then analyzed through the use of multi-scale, areal, and complexity analyses. Correlations between energy and relative area, and between energy and area-scale complexity, were tested using linear regression analyses at many different scales. The strengths of the correlations were then analyzed to discern any trends with respect to scale. The correlations between discharge energies and conventional height parameters were also tested, as were the correlations with smooth-rough crossovers. The latter were calculated from area-scale analysis (outlined below).

Surfaces were created on 316L stainless steel using μEDM technology based on a resistive-capacitive circuit system in which different discharge pulse energies are selected by the size of the capacitor in the circuit. If the system fully discharges and recovers before discharging again, the theoretical energy generated is as given in Table 1. This energy determines the maximum material removal rate.

Table 1. Capacitance and potential discharge energies.

The values used in this study represent the most common energies used when manufacturing micro-EDM parts. The tool electrode was formed by pulling a 99.99% tungsten wire with a 3000 rpm spinning mandrel cylinder. The μEDM energy levels used for this study (Figure 1) illustrate that higher capacitance produces a lower natural frequency for the circuit and creates a more energetic discharge.

Figure 1. Image rendered from a surface μEDM-machined with 16 500nJ discharge pulses (100x objective, no zoom). All units in micrometers.

The μEDM-machined surfaces were measured using the LEXT OLS4000, with all measurements made with a 100× objective lens with a numerical aperture (NA) of 0.95 and a 405 nm wavelength laser. Each surface was measured four times over a region of 128×128 μm collecting a 1024×1024 sampling of elevations in each measurement. The sampling interval was approximately 125 nm when no zoom was used (surfaces were measured with no zoom for the analyses). All surfaces were also observed with a 100× objective with zoom of 8×, resulting in the observation of a 16×16 μm region with a sampling interval of approximately 16 nm.

Surface measurements were processed using form removal and modal outlier filtering. Conventional height parameters were also determined.

Figure 2. Image rendered from a surface μEDM-machined with 16 500nJ discharge pulses (100x objective, 8x zoom). All units in micrometers.

Area-scale and complexity scale analyses (ASME B46.1 2009, ISO 25178-2 2012) were performed on the filtered files. Relative surface areas were evaluated over the areal scales available in the measurement, from half the region measured (8,192 m2) to half the square of the sampling interval (0.0078 m2).

The correlations of the relative areas and the area-scale fractal complexities were determined using linear regressions at each of the analyzed scales. Regression coefficients (R2) were determined from linear regression analyses when performed on conventional height parameters and SRCs with respect to discharge energies.


Table 2. Areal height parameters varying with discharge pulse energy.

Areal height parameters including peak-to-valley height, peak height, and valley depth (Sz, Sp, and Sv); the arithmetic average roughness and root mean square roughness (Sa and Sq); and the skew and kurtosis (Ssk and Sku), are listed in Table 2. Height parameters and average heights all tended to increase with increasing μEDM energy. Skew and kurtosis did not appear to show any clear trend. A regression analysis for these same parameters is shown in Table 3.

Table 3. Regression analysis of height parameters as a function of discharge pulse energy.

Images rendered from surface measurements created at the highest energy μEDM (16 500nJ) are shown in Figures 1 and 2 (no zoom and 8× zoom, respectively). What appear to be craters formed by discharge pulses can be seen as visible depressions in Figure 1. The image created with 8× zoom (Figure 2) features a distinct ridge that shows the limits of the crater.

Figure 3. Image rendered from a surface μEDM-machined with 320nJ discharge pulses (100x objective, no zoom). All units in micrometers.

Figures 3 and 4 show images rendered from measurements made of surfaces created with 320nJ discharge pulses (no zoom and 8× zoom, respectively). In Figure 3, with no zoom, the craters are considerably smaller and are less distinct than on surfaces created at higher energies. In Figure 4, with 8× zoom, the largest crater features appear to be just less than 2 μm in diameter. No ridges are evident at the edges of these craters, as there were with surfaces created at higher energy discharges. Smaller features, possibly pores or craters, are also evident at the edges of the craters. The interiors of the larger craters do not show the same wavy terraces evident in the surfaces created with 16 500nJ discharge pulses. Rather, at the center of the craters formed with 320nJ pulses there are small, relatively smooth regions.

Figure 4. Image rendered from a surface μEDM-machined with 320nJ discharge pulses (100x objective, 8× zoom). Units on vertical axis in nanometers; all others in micrometers.

Figures 5 and 6 show images rendered from measurements made of surfaces created with 18nJ discharge pulses (no zoom, 8× zoom). The image with no zoom is carpeted with a fine-scale textured surface with features around 100 nm. In Figure 6, with 8× zoom, the surface is dominated by small bumps, similar to those at the edges of craters created with 320nJ discharge pulses. There are also some craters evident with relatively smooth centers, similar to those created with 320nJ pulses.

Figure 5. Image rendered from a surface μEDM-machined with 18nJ discharge pulses (100x objective, no zoom). All units in micrometers.
Figure 6. Image rendered from a surface μEDM-machined with 18nJ discharge pulses (100x objective, 8x zoom). Units on the vertical axis in nanometers; all others in micrometers.

Table 4 shows the mean SRCs (smooth-rough crossovers) for all energies. SRCs were computed using thresholds in relative areas based on 2.5%, 5%, and 10% of the greatest relative area calculated for that surface (ASME B46.1 2009).

Table 4. Discharge pulse energies and means of smooth-rough crossovers (SRCs) for each surface.

Coefficients of regression (R2) for linear regression of SRCs are shown in Table 5. All three thresholds provide SRCs that have regression coefficients greater than 0.98, significantly stronger than the regressions with conventional height parameters.

Table 5. Regression coefficients (R2) for SRCs based on different thresholds in relative area (regressed linearly with discharge pulse energies).

The ability to discriminate between μEDM-machined surfaces with 95% or greater confidence (F-Test) is summarized in Table 6.

Table 6. F-Tests: Scale range in μm2 for discrimination with at least 95% confidence.


Laser scanning confocal microscopy can be used to precisely measure the topographies of stainless-steel surfaces machined by EDM with different discharge pulse energies to scales of 200 nm laterally and tens of nanometers vertically. On the EDM-machined surfaces measured with confocal microscopy in this study:

  • Height texture characterization parameters correlated well with discharge pulse energies. The R2 values were between 0.81 and 0.93.

  • Skew and kurtosis did not correlate well with discharge pulse energies. The R2 values were less than 0.15.

  • The relative area and the area-scale fractal complexities were able to discriminate their surfaces with greater than 95% confidence over a minimum range in scale between 0.1 and 10 μm2 up to a range of 0.01 and 500 μm2.

  • The strongest correlations were found using multi-scale areal analysis:

    • The SRCs correlated with the discharge pulse energy with R2 values of 0.98 and 0.99.

    • The relative area correlated with the discharge pulse energy with an R2 = 0.98, 10, and 100 μm2.

    • The complexity correlated with the discharge pulse energy with an R2 = 0.97 between scales of 100 and 200 μm2.


Several types of features consistent with known EDM mechanisms are discernible on images rendered with the Olympus LEXT OLS4000 on surfaces created by μEDM. The measured surfaces created with different pulse energies can be discriminated clearly over wide ranges of scales using area-scale analysis. Strong correlations were found between the discharge pulse energies with which the surfaces were created and calculated texture characterization parameters. The strongest correlations were found with the SRC scales, the relative area, and the area-scale fractal complexity.

This article was written by Dr. Christopher A. Brown and Dr. Joyce M. Hyde of the Worcester Polytechnic Institute (Worcester, MA) and Jonathan Montgomery of SmalTec International (Lisle, IL). For more information, contact Dr. Brown at This email address is being protected from spambots. You need JavaScript enabled to view it. or visit here .