## 3 Experiment and Discussion
### Effect of Elastic Recovery  
The effect of elastic recovery of the reverse cutting edge artifact on cutting edge radius measurement accuracy was analyzed. An AFM cantilever (OMCL-AC240 TS, Olympus, Tokyo, Japan) with a nominal tip radius of 7 nm and a tip height of 14 \(\upmu\)m was selected to measure the topographies of the actual and the reverse diamond tool cutting edge. A single point diamond tool with a nose radius of 1 mm was measured in this test. Figure 4: Copper workpiece. (**a**) Atomic force microscope (AFM) topography; (**b**) Roughness of the section A–A’. Figure 3: Principle of replicating the tool cutting edge using the proposed nanoindentation system. (**a**) Motion of the diamond tool; (**b**) Outputs of two sensors. Since the indentation depth and the elastic recovery of the reverse cutting edge artifact are related with each other based on the Hertz theory, a group of reverse cutting edge artifacts with various indentation depths from 20 to 180 nm were fabricated on the designed nanoindentation system in order to investigate the effect of the elastic recovery. The interval of indentation depth was set at approximately 20 nm. Figure 5 shows the outputs of the inside and the outside sensors when the command displacement of the diamond tool actuated by the FTS was set at 50 nm. Only the outputs in step three of Figure 3 are plotted in Figure 5. The output of the inside sensor was 52 nm, which was approximately the same as the command displacement of the diamond tool. The output of the outside sensor was 27 nm. The indentation depth of the reverse cutting edge artifact was calculated to be 25 nm by substituting the outputs of two sensors into Equation (5). The diamond tool was positioned on the \(Z\)-scanner of the AFM with the bisector of the included angle between its rake face and clearance face. The Olympus AFM cantilever was moved along the \(X\)-, \(Y\)- and \(Z\)-directions by the \(XY\)-stage and the \(Z\)-scanner of the AFM to make the alignment between the AFM tip and the apex of the diamond tool cutting edge. The actual cutting edge was, then, scanned by the AFM cantilever. The scan range and the scan rate were set to be 2 \(\upmu\)m (\(X\)) \(\times\) 2 \(\upmu\)m (\(Y\)) and 1.2 \(\upmu\)m/s, respectively. The numbers of scanning lines in the \(X\)- and \(Y\)-positions were 1024 and 1024, respectively. Figure 6a shows a 3D topography of the diamond tool cutting edge. It can be seen from the figure that there was a clear edge between the rake face and the clearance face, which can be employed for quantitative evaluation of the diamond tool cutting edge radius. The cross-sectional profile extracted from the 3D topography is shown in Figure 6b. The measured tool cutting edge radius was obtained from that of the fitted arc, which was evaluated by fitting the points in the apex of the cross-sectional profile of the cutting edge based on the least square method. The radius of the fitted arc, referred to as \(R_{\text{tool\_m}}\), was evaluated to be approximately 40.32 nm. It should be noted that the fitted arc was a geometric convolution of the AFM tip and the actual diamond tool cutting edge. Therefore, the value of 40.32 nm was not the actual diamond tool cutting edge radius. Figure 5: The outputs of the inside and the outside sensors with a command displacement of 50 nm. The reverse cutting edge artifact was also placed on the \(Z\)-scanner of the AFM. The same AFM cantilever, which had been used to scan the actual cutting edge, was brought to scan the reverse cutting edge. The scanning range, the scan rate, and the number of scanning lines in the \(X\)- and \(Y\)-position were set to be the same as those in the AFM measurement of the actual cutting edge. Figure 7a,b shows the AFM topography and the cross-sectional profile of the reverse cutting edge artifact, respectively. It can be seen from Figure 7a that the reverse cutting edge was well transcribed from the geometry of the diamond tool. The depth of the reverse cutting edge artifact was evaluated to be 28 nm.