## 2 Principle of Measuring Cutting Edge Radius
The difference is small and is negligible for the cutting edge radius measurement as compared with the cutting edge radius. However, when the indentation depth is set to be 200 nm, the measurement uncertainty in the tool cutting edge radius measurement becomes large. Therefore, the indentation depth should be controlled within a range of 20 to 200 nm. A nanoindentation system is, then, designed for achieving the requirement of high-precision indentation depth control of the reverse cutting edge artifact as shown in Figure 2. A single point diamond tool is mounted on the FTS to indent into a prepolished metal workpiece by a linear stage and/or the FTS. When the distance between the diamond tool tip and the workpiece surface is larger than the motion stroke of the FTS, the linear stage is employed to move the diamond tool to approach the workpiece surface by a steeping motor controller. The displacement of the diamond tool driven by the linear stage and the FTS can be measured by the linear encoder of the stage and the displacement sensor of the FTS unit (inside sensor). The workpiece is attached on a cantilever. One end of the cantilever is fixed on a holder and the other end is preloaded by a preload controller. An outside displacement sensor (outside sensor) is used to detect the deflection of the cantilever caused by the indentation. Two \(XY\)-manual stages (Stage 1 and Stage 2) are used for the alignment between the workpiece surface and the diamond tool tip. The outputs of two sensors are collected by an oscilloscope for further evaluating the indentation depth \(d_{\text{depth}}\) based on the following equation:  
\[d_{\text{depth}}=d_{\text{in}}-d_{\text{out}} \tag{5}\]  
where \(d_{\text{in}}\) and \(d_{\text{out}}\) represent the outputs of the inside and the outside sensors, respectively. The operation of the nanoindentation system is optimized for achieving high-precision control of the indentation depth during the tool cutting edge replication, as shown in Figure 1.0 There are three steps for replicating the cutting-edge geometry of a diamond tool into a workpiece surface. In step one, the linear stage is firstly used to move the diamond tool to the initial position shown in Figure 3a, where the distance between the diamond tool tip and the workpiece surface is equal to the motion stroke of the FTS. Then, the diamond tool is actuated by the FTS with a step of 5 nm to avoid any unexpected contact damages on the workpiece surface. The output of the outside sensor does not change in this step, as shown in Figure 3b. In step two, the contact between the diamond tool and the workpiece is established at the contact position where the output of the outside sensor starts to vary due to the deflection of the cantilever. A small indentation mark with a depth less than 5 nm is generated on the workpiece surface, which is small as compared with the reverse cutting edge. Therefore, the effect of the small indentation mark can be ignored. In step three, the diamond tool is indented into the workpiece surface with the command indentation depth, which can be evaluated by substituting the outputs of two sensors at the indentation position into Equation (5). Therefore, a reverse cutting edge artifact with a high-precision depth is fabricated by following these three steps. Figure 1.1 _Cont._  
Figure 1.2 Schematic of the nanoindentation system.