high-precision cutting edge radius measurement of single
TRANSCRIPT
applied sciences
Article
High-Precision Cutting Edge Radius Measurement ofSingle Point Diamond Tools Using an Atomic ForceMicroscope and a Reverse Cutting Edge Artifact
Kai Zhang 1, Yindi Cai 2,* , Yuki Shimizu 1 , Hiraku Matsukuma 1 and Wei Gao 1
1 Precision Nanometrology Laboratory, Department of Finemechanics, Tohoku University,Sendai 980-8579, Japan; [email protected] (K.Z.);[email protected] (Y.S.); [email protected] (H.M.);[email protected] (W.G.)
2 Key Laboratory for Micro/Nano Technology and System of Liaoning Province,Dalian University of Technology, Dalian 116024, China
* Correspondence: [email protected]
Received: 28 May 2020; Accepted: 6 July 2020; Published: 13 July 2020�����������������
Abstract: This paper presents a measurement method for high-precision cutting edge radius of singlepoint diamond tools using an atomic force microscope (AFM) and a reverse cutting edge artifactbased on the edge reversal method. Reverse cutting edge artifact is fabricated by indenting a diamondtool into a soft metal workpiece with the bisector of the included angle between the tool’s rake faceand clearance face perpendicular to the workpiece surface on a newly designed nanoindentationsystem. An AFM is applied to measure the topographies of the actual and the reverse diamond toolcutting edges. With the proposed edge reversal method, a cutting edge radius can be accuratelyevaluated based on two AFM topographies, from which the convolution effect of the AFM tip can bereduced. The accuracy of the measurement of cutting edge radius is significantly influenced by thegeometric accuracy of reverse cutting edge artifact in the proposed measurement method. In thenanoindentation system, the system operation is optimized for achieving high-precision control ofthe indentation depth of reverse cutting edFigurege artifact. The influence of elastic recovery andthe AFM cantilever tip radius on the accuracy of cutting edge radius measurement are investigated.Diamond tools with different nose radii are also measured. The reliability and capability of theproposed measurement method for cutting edge radius and the designed nanoindentation system aredemonstrated through a series of experiments.
Keywords: single point diamond tool; cutting edge radius; reversal method; nanoindentation system;elastic recovery
1. Introduction
Ultra-precision diamond cutting, combining a single point diamond tool with an ultra-precisionlathe, has been widely employed for the fabrication of microstructure elements, such as microlensarrays [1], compound eye freeform surfaces [2], and sinusoidal grids [3,4]. The achievable machiningaccuracy of the ultra-precision diamond cutting is significantly affected by the geometry of the diamondtool, including cutting edge contour, cutting edge radius, and tool faces [5–7]. In order to achieve ananometric machining accuracy, it is essential to conduct a quantitative evaluation of the geometry ofthe diamond tool, especially cutting edge radius, which determines the minimum depth of cut and thesurface finish of the machined microstructures [8,9].
Cutting edge radius of a diamond tool is usually required to be within 10 to 100 nm forultra-precision diamond cutting [10]. Therefore, the methods for cutting edge radius measurement
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should have a nanometric measurement accuracy in both lateral and vertical directions [11].Optical methods can conduct fast and non-contact measurements [12–14]. However, a lateral resolutionthat is larger than 10 nm is limited by the optical diffraction phenomenon which occurs around thecutting edge when an optical method is used to measure the geometry of the diamond tool. Scanningelectron microscopes (SEMs) have a nanometric lateral resolution and a wide view field [15]. However,because SEMs have a limitation of two-dimensional (2D) projection, they can only be used for thequalitative evaluation of diamond tool cutting edge radius and cannot be used for the quantitativeevaluation. In addition, the material of diamond tools also influences the measurement accuracy ofthe diamond tool cutting edge radius using SEMs [16]. Atomic force microscopes (AFMs), which canprovide a three-dimensional (3D) measurement with a nanometric accuracy in both lateral and verticaldirections, can directly measure the diamond tool cutting edge radius by accurately aligning the AFMcantilever tip with the diamond tool cutting edge within the measurement range of the AFM [17–19].However, the process for an accurate alignment is extremely time-consuming and the AFM cantilevertip can also be easily damaged due to an inaccurate alignment operation.
An indirect measurement method based on an AFM has been proposed to address the aboveproblems using an AFM to measure cutting edge radius of a diamond tool [20]. A profile of a diamondtool cutting edge is copied on a copper workpiece by indenting the diamond tool into the workpieceon an ultra-precision lathe. Then, the copied profile is scanned by an AFM, from which the diamondtool cutting edge radius can be obtained. Since this indirect measurement method can protect thediamond tool and the AFM cantilever tip from damage, and also shorten the measurement time, it isattractive for practical applications. However, the elastic recovery of the copied profile can affectthe measurement accuracy, which is not considered in the indirect measurement method based onthe AFM. More importantly, since both the direct and indirect measurement methods are based onan AFM, the obtained profile is a geometric convolution of the AFM tip and the actual and copieddiamond tool cutting edges. It is essential to eliminate the convolution effect of the AFM tip whosesize is comparable to that of the diamond tool cutting edge, for achieving a high-precision diamondtool cutting edge radius measurement.
There are two approaches for reducing the convolution effect of the AFM tip. One approach is todirectly characterize the AFM tip with a form surface measuring instrument. The other is to makean error separation operation on the AFM images for removing the influence of the AFM tip profile.Compared with the direct characterization approach, the error separation approach is more effectivebecause no additional form surface measuring instruments are necessary [21]. An edge reversal errorseparation method based on an AFM was proposed for measuring cutting edge radius of diamond toolwithout the effect of the AFM tip radius by the authors of [22]. Firstly, a replicated cutting edge wasobtained by indenting a diamond tool into a soft metal material. Then, an AFM was applied to scanthe actual and the replicated cutting edges. The cutting edge radius of the diamond tool was obtainedby taking the difference between the AFM images of the actual and the replicated cutting edges whenthe elastic recovery of the replicated cutting edge was small as compared with the cutting edge radius.Molecular dynamics (MD) simulations were carried out to investigate the effect of elastic recovery oncutting edge radius in our previous researches [23,24]. It was verified that when the indentation depthof the replicated cutting edge was set to be larger than 200 nm, the elastic recovery of the replicatedcutting edge could be ignored. However, a large indentation depth would cause more measurementuncertainties in the AFM measurement of the replicated tool cutting edge.
Meanwhile, a nanoindentation instrument has been designed for replicating the diamond toolcutting edge onto a soft workpiece surface [25]. The displacement of the diamond tool was monitoredby a capacitive sensor of a fast tool servo (FTS) unit, which was employed to drive the diamondtool. The workpiece was pasted on a cantilever whose deflection was detected by another capacitivesensor. The indentation depth of the diamond tool was obtained from the outputs of the two capacitivesensors. However, it was a time-consuming process to replicate the diamond tool cutting edge usingthis nanoindentation instrument. In addition, a contact damage would be generated on the workpiece
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surface when the tool-workpiece contact was established before the replication. The contact damagewould influence the indentation depth and the profile of the replicated cutting edge.
In this paper, we present high-precision cutting edge radius measurements of single point diamondtools using an AFM and a reverse cutting edge artifact based on the proposed edge reversal method andthe designed nanoindentation system. After introducing the measurement principles, the operationof the nanoindentation system is optimized for achieving high-precision control of the indentationdepth. The effects of the elastic recovery and the AFM cantilever tip on the measurement accuracy andthe measurement uncertainty are investigated. A series of experiments are preformed to verify thereliability and the capability of the proposed method and the designed system.
2. Principle of Measuring Cutting Edge Radius
There are three steps in the process of measuring the diamond tool cutting edge radius using theproposed edge reversal method, as shown in Figure 1.
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In this paper, we present high-precision cutting edge radius measurements of single point 95 diamond tools using an AFM and a reverse cutting edge artifact based on the proposed edge reversal 96 method and the designed nanoindentation system. After introducing the measurement principles, 97 the operation of the nanoindentation system is optimized for achieving high-precision control of the 98 indentation depth. The effects of the elastic recovery and the AFM cantilever tip on the measurement 99 accuracy and the measurement uncertainty are investigated. A series of experiments are preformed 100 to verify the reliability and the capability of the proposed method and the designed system. 101
2. Principle of Measuring Cutting Edge Radius 102 There are three steps in the process of measuring the diamond tool cutting edge radius using the 103
proposed edge reversal method, as shown in Figure 1. 104
105 Figure 1. Principle of the proposed edge reversal method. 106
The first step is related to the cutting-edge replication shown in Figure 1. The single point 107 diamond tool, a piece of copper workpiece, and a nanoindentation system are employed. An 108 indentation mark, referred to as the reverse cutting edge artifact, is fabricated by indenting the 109 diamond tool into the workpiece with the bisector of the included angle between its rake face and 110 clearance face perpendicular to the workpiece surface using the nanoindentation system. The 111 configuration and the principle of the nanoindentation system is introduced later. The reverse cutting 112 edge artifact is, thus, directly transcribed from the geometry of the diamond tool. 113
The second step is related to the AFM measurement of the actual cutting edge of the diamond 114 tool. The diamond tool, with the cutting edge radius, Rtool, is positioned under the AFM cantilever 115 with the bisector of the included angle between its rake face and clearance face along the vertical axis. 116 An AFM cantilever is moved by an XY-stage and a Z-scanner of the AFM along the X-, Y- and Z-117 directions to align the AFM cantilever tip with the apex of the diamond tool cutting edge. After an 118 accurate alignment, the AFM cantilever is brought to scan across the diamond tool cutting edge. Since 119 the tip radius Rtip of the AFM cantilever is comparable to the cutting edge radius, Rtool, of the diamond 120 tool, the scan trace of the AFM with an apex radius of Rtool_m is a convolution of the AFM tip and the 121 diamond tool cutting edge, as shown in Figure 1. Therefore, the following equation can be obtained: 122
tiptoolmtool RRR +=_ (1)
The third step is related to the AFM measurement of the reverse cutting edge artifact. Then, the 123 reverse cutting edge artifact is measured by the AFM. The apex radius of the reverse cutting edge is 124 defined as Rmark, which is also comparable to the AFM tip radius Rtip. After the alignment between 125 the AFM cantilever tip and the apex of reverse cutting edge, the AFM tip scans across the reverse 126
Figure 1. Principle of the proposed edge reversal method.
The first step is related to the cutting-edge replication shown in Figure 1. The single point diamondtool, a piece of copper workpiece, and a nanoindentation system are employed. An indentationmark, referred to as the reverse cutting edge artifact, is fabricated by indenting the diamond toolinto the workpiece with the bisector of the included angle between its rake face and clearance faceperpendicular to the workpiece surface using the nanoindentation system. The configuration and theprinciple of the nanoindentation system is introduced later. The reverse cutting edge artifact is, thus,directly transcribed from the geometry of the diamond tool.
The second step is related to the AFM measurement of the actual cutting edge of the diamond tool.The diamond tool, with the cutting edge radius, Rtool, is positioned under the AFM cantilever with thebisector of the included angle between its rake face and clearance face along the vertical axis. An AFMcantilever is moved by an XY-stage and a Z-scanner of the AFM along the X-, Y- and Z-directionsto align the AFM cantilever tip with the apex of the diamond tool cutting edge. After an accuratealignment, the AFM cantilever is brought to scan across the diamond tool cutting edge. Since thetip radius Rtip of the AFM cantilever is comparable to the cutting edge radius, Rtool, of the diamondtool, the scan trace of the AFM with an apex radius of Rtool_m is a convolution of the AFM tip and thediamond tool cutting edge, as shown in Figure 1. Therefore, the following equation can be obtained:
Rtool_m = Rtool + Rtip (1)
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The third step is related to the AFM measurement of the reverse cutting edge artifact. Then,the reverse cutting edge artifact is measured by the AFM. The apex radius of the reverse cutting edgeis defined as Rmark, which is also comparable to the AFM tip radius Rtip. After the alignment betweenthe AFM cantilever tip and the apex of reverse cutting edge, the AFM tip scans across the reversecutting edge artifact to map out its topography. The scanned image is also a convolution of the AFMtip and the reverse cutting edge artifact. Therefore, the following equation can be obtained:
Rmark_m = Rmark −Rtip (2)
The copper workpiece surface displays a certain degree of elastic recovery after the diamond toolis withdrawn from the surface in the nanoindentation process [23,24]. The relationship between theactual cutting edge radius and reverse cutting edge radius can be expressed as:
Rtool = (1− ξ)Rmark (3)
where ξ represents the elastic recovery coefficient of the reverse cutting edge artifact. According toEquations (1)–(3), cutting edge radius of the diamond tool can be evaluated to be:
Rtool =1
2− ξ(Rtool_m + Rmark_m) (4)
Therefore, cutting edge radius of the diamond tool can be obtained without being influenced bythe AFM tip radius. As can be seen from Equation (4), the achievable accuracy of this method dependson the elastic recovery coefficient ξ. It has been verified that the elastic recovery coefficient, ξ, of thereverse cutting edge would be reduced to 0.012 from 0.068 when the indentation depth was increasedto 20 nm from 2.5 nm based on molecular dynamics (MD) simulations [22]. The detail of the MDsimulation can be found in [22] and is not repeated in this paper for the sake of clarity. The differencebetween Rmark and Rtool was evaluated to be 0.24 nm when the indentation depth was set to be 200 nm.The difference is small and is negligible for the cutting edge radius measurement as compared withthe cutting edge radius. However, when the indentation depth is set to be 200 nm, the measurementuncertainty in the tool cutting edge radius measurement becomes large. Therefore, the indentationdepth should be controlled within a range of 20 to 200 nm.
A nanoindentation system is, then, designed for achieving the requirement of high-precisionindentation depth control of the reverse cutting edge artifact as shown in Figure 2. A single pointdiamond tool is mounted on the FTS to indent into a prepolished metal workpiece by a linear stageand/or the FTS. When the distance between the diamond tool tip and the workpiece surface is largerthan the motion stroke of the FTS, the linear stage is employed to move the diamond tool to approachthe workpiece surface by a steeping motor controller. The displacement of the diamond tool driven bythe linear stage and the FTS can be measured by the linear encoder of the stage and the displacementsensor of the FTS unit (inside sensor). The workpiece is attached on a cantilever. One end of thecantilever is fixed on a holder and the other end is preloaded by a preload controller. An outsidedisplacement sensor (outside sensor) is used to detect the deflection of the cantilever caused by theindentation. Two XY-manual stages (Stage 1 and Stage 2) are used for the alignment between theworkpiece surface and the diamond tool tip. The outputs of two sensors are collected by an oscilloscopefor further evaluating the indentation depth ddepth based on the following equation:
ddepth = din − dout (5)
where din and dout represent the outputs of the inside and the outside sensors, respectively.
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cutting edge artifact to map out its topography. The scanned image is also a convolution of the AFM 127 tip and the reverse cutting edge artifact. Therefore, the following equation can be obtained: 128
tipmarkmmark RRR −=_ (2)
The copper workpiece surface displays a certain degree of elastic recovery after the diamond 129 tool is withdrawn from the surface in the nanoindentation process [23,24]. The relationship between 130 the actual cutting edge radius and reverse cutting edge radius can be expressed as: 131
marktool RR )1( ξ−= (3)
where ξ represents the elastic recovery coefficient of the reverse cutting edge artifact. According to 132 Equations (1)–(3), cutting edge radius of the diamond tool can be evaluated to be: 133
)(2
1__ mmarkmtooltool RRR +
−=
ξ (4)
Therefore, cutting edge radius of the diamond tool can be obtained without being influenced by 134 the AFM tip radius. As can be seen from Equation (4), the achievable accuracy of this method depends 135 on the elastic recovery coefficient ξ. It has been verified that the elastic recovery coefficient, ξ, of the 136 reverse cutting edge would be reduced to 0.012 from 0.068 when the indentation depth was increased 137 to 20 nm from 2.5 nm based on molecular dynamics (MD) simulations [22]. The detail of the MD 138 simulation can be found in [22] and is not repeated in this paper for the sake of clarity. The difference 139 between Rmark and Rtool was evaluated to be 0.24 nm when the indentation depth was set to be 200 nm. 140 The difference is small and is negligible for the cutting edge radius measurement as compared with 141 the cutting edge radius. However, when the indentation depth is set to be 200 nm, the measurement 142 uncertainty in the tool cutting edge radius measurement becomes large. Therefore, the indentation 143 depth should be controlled within a range of 20 to 200 nm. 144
A nanoindentation system is, then, designed for achieving the requirement of high-precision 145 indentation depth control of the reverse cutting edge artifact as shown in Figure 2. A single point 146 diamond tool is mounted on the FTS to indent into a prepolished metal workpiece by a linear stage 147 and/or the FTS. When the distance between the diamond tool tip and the workpiece surface is larger 148 than the motion stroke of the FTS, the linear stage is employed to move the diamond tool to approach 149 the workpiece surface by a steeping motor controller. The displacement of the diamond tool driven 150 by the linear stage and the FTS can be measured by the linear encoder of the stage and the 151 displacement sensor of the FTS unit (inside sensor). The workpiece is attached on a cantilever. One 152 end of the cantilever is fixed on a holder and the other end is preloaded by a preload controller. An 153 outside displacement sensor (outside sensor) is used to detect the deflection of the cantilever caused 154 by the indentation. Two XY-manual stages (Stage 1 and Stage 2) are used for the alignment between 155 the workpiece surface and the diamond tool tip. The outputs of two sensors are collected by an 156 oscilloscope for further evaluating the indentation depth ddepth based on the following equation: 157
158 PC
Sensor amplifier Oscilloscope Sensor
amplifier
D/AOutside sensor
Stage 2
Stage 1
Linear stage
FTS
Diamond tool
Workpiece
Cantilever
XZY
Motor Controller
Preload controller
Holder
Figure 2. Schematic of the nanoindentation system.
The operation of the nanoindentation system is optimized for achieving high-precision control ofthe indentation depth during the tool cutting edge replication, as shown in Figure 3. There are threesteps for replicating the cutting-edge geometry of a diamond tool into a workpiece surface. In stepone, 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 motionstroke of the FTS. Then, the diamond tool is actuated by the FTS with a step of 5 nm to avoid anyunexpected contact damages on the workpiece surface. The output of the outside sensor does notchange in this step, as shown in Figure 3b. In step two, the contact between the diamond tool andthe workpiece is established at the contact position where the output of the outside sensor starts tovary due to the deflection of the cantilever. A small indentation mark with a depth less than 5 nmis 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 isindented into the workpiece surface with the command indentation depth, which can be evaluatedby 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.
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Figure 2. Schematic of the nanoindentation system. 159
outindepth ddd −= (5)
where din and dout represent the outputs of the inside and the outside sensors, respectively. 160 The operation of the nanoindentation system is optimized for achieving high-precision control 161
of the indentation depth during the tool cutting edge replication, as shown in Figure 3. There are 162 three steps for replicating the cutting-edge geometry of a diamond tool into a workpiece surface. In 163 step one, the linear stage is firstly used to move the diamond tool to the initial position shown in 164 Figure 3a, where the distance between the diamond tool tip and the workpiece surface is equal to the 165 motion stroke of the FTS. Then, the diamond tool is actuated by the FTS with a step of 5 nm to avoid 166 any unexpected contact damages on the workpiece surface. The output of the outside sensor does not 167 change in this step, as shown in Figure 3b. In step two, the contact between the diamond tool and the 168 workpiece is established at the contact position where the output of the outside sensor starts to vary 169 due to the deflection of the cantilever. A small indentation mark with a depth less than 5 nm is 170 generated on the workpiece surface, which is small as compared with the reverse cutting edge. 171 Therefore, the effect of the small indentation mark can be ignored. In step three, the diamond tool is 172 indented into the workpiece surface with the command indentation depth, which can be evaluated 173 by substituting the outputs of two sensors at the indentation position into Equation (5). Therefore, a 174 reverse cutting edge artifact with a high-precision depth is fabricated by following these three steps. 175
176
177 Figure 3. Principle of replicating the tool cutting edge using the proposed nanoindentation system. 178 (a) Motion of the diamond tool; (b) Outputs of two sensors. 179
3. Experiment and Discussion 180
Inside sensor
Z XY
Outside sensor Diamond
tool
Cantilever
din
Workpieceddepth
dout
Holder
Holder
Initial position
Step 1Step 2
Step 3
(a)
Contact position
Indentation position
Time
Out
put o
f sen
sor Outside sensor
Inside sensor
din
5 nm≤ 5 nm
Step 1 Step 2 Step 3(b)
Figure 3. Cont.
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Figure 2. Schematic of the nanoindentation system. 159
outindepth ddd −= (5)
where din and dout represent the outputs of the inside and the outside sensors, respectively. 160 The operation of the nanoindentation system is optimized for achieving high-precision control 161
of the indentation depth during the tool cutting edge replication, as shown in Figure 3. There are 162 three steps for replicating the cutting-edge geometry of a diamond tool into a workpiece surface. In 163 step one, the linear stage is firstly used to move the diamond tool to the initial position shown in 164 Figure 3a, where the distance between the diamond tool tip and the workpiece surface is equal to the 165 motion stroke of the FTS. Then, the diamond tool is actuated by the FTS with a step of 5 nm to avoid 166 any unexpected contact damages on the workpiece surface. The output of the outside sensor does not 167 change in this step, as shown in Figure 3b. In step two, the contact between the diamond tool and the 168 workpiece is established at the contact position where the output of the outside sensor starts to vary 169 due to the deflection of the cantilever. A small indentation mark with a depth less than 5 nm is 170 generated on the workpiece surface, which is small as compared with the reverse cutting edge. 171 Therefore, the effect of the small indentation mark can be ignored. In step three, the diamond tool is 172 indented into the workpiece surface with the command indentation depth, which can be evaluated 173 by substituting the outputs of two sensors at the indentation position into Equation (5). Therefore, a 174 reverse cutting edge artifact with a high-precision depth is fabricated by following these three steps. 175
176
177 Figure 3. Principle of replicating the tool cutting edge using the proposed nanoindentation system. 178 (a) Motion of the diamond tool; (b) Outputs of two sensors. 179
3. Experiment and Discussion 180
Inside sensor
Z XY
Outside sensor Diamond
tool
Cantilever
din
Workpieceddepth
dout
Holder
Holder
Initial position
Step 1Step 2
Step 3
(a)
Contact position
Indentation position
Time
Out
put o
f sen
sor Outside sensor
Inside sensor
din
5 nm≤ 5 nm
Step 1 Step 2 Step 3(b)
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.
3. Experiment and Discussion
A series of experiments were performed to investigate the effect of elastic recovery on the reversecutting edge artifact and the AFM cantilever tip on the measurement accuracy of the cutting edgeradius as well as to verify the reliability of the proposed edge reversal method and the capability of thedesigned nanoindentation system.
Since copper has a relatively large Young’s modulus, a prepolished copper workpiece with a sizeof 10 mm (length) × 10 mm (width) × 2 mm (thickness) was selected as the workpiece. Figure 4ashows the topography of the copper workpiece surface measured by a commercial AFM (Innova,Bruker, Billerica, MA, USA). As shown in Figure 4b, the Root Mean Square (RMS) roughness of thesection A–A’ of the copper workpiece was evaluated to be 2.43 nm based on a 3D AFM topography.The workpiece surface was smooth enough for replicating the diamond tool cutting edge geometry.The copper workpiece was pasted on an aluminum cantilever with a spring constant of 155 N/m at thecontact point. The deformation of the aluminum cantilever was detected by a capacitive sensor (6800,MicroSense, Lowell, MA, USA).
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A series of experiments were performed to investigate the effect of elastic recovery on the reverse 181 cutting edge artifact and the AFM cantilever tip on the measurement accuracy of the cutting edge 182 radius as well as to verify the reliability of the proposed edge reversal method and the capability of 183 the designed nanoindentation system. 184
Since copper has a relatively large Young’s modulus, a prepolished copper workpiece with a 185 size of 10 mm (length) × 10 mm (width) × 2 mm (thickness) was selected as the workpiece. Figure 4a 186 shows the topography of the copper workpiece surface measured by a commercial AFM (Innova, 187 Bruker, Billerica, USA). As shown in Figure 4b, the Root Mean Square (RMS) roughness of the section 188 A–A’ of the copper workpiece was evaluated to be 2.43 nm based on a 3D AFM topography. The 189 workpiece surface was smooth enough for replicating the diamond tool cutting edge geometry. The 190 copper workpiece was pasted on an aluminum cantilever with a spring constant of 155 N/m at the 191 contact point. The deformation of the aluminum cantilever was detected by a capacitive sensor (6800, 192 MicroSense, Lowell, Massachusetts, USA). 193
194 Figure 4. Copper workpiece. (a) Atomic force microscope (AFM) topography; (b) Roughness of the 195
section A–A’. 196
3.1. Effect of Elastic Recovery 197 The effect of elastic recovery of the reverse cutting edge artifact on cutting edge radius 198
measurement accuracy was analyzed. An AFM cantilever (OMCL-AC240TS, Olympus, Tokyo, Japan) 199 with a nominal tip radius of 7 nm and a tip height of 14 μm was selected to measure the topographies 200 of the actual and the reverse diamond tool cutting edge. A single point diamond tool with a nose 201 radius of 1 mm was measured in this test. 202
Since the indentation depth and the elastic recovery of the reverse cutting edge artifact are 203 related with each other based on the Hertz theory, a group of reverse cutting edge artifacts with 204 various indentation depths from 20 to 180 nm were fabricated on the designed nanoindentation 205 system in order to investigate the effect of the elastic recovery. The interval of indentation depth was 206 set at approximately 20 nm. 207
Figure 5 shows the outputs of the inside and the outside sensors when the command 208 displacement of the diamond tool actuated by the FTS was set at 50 nm. Only the outputs in step 209 three of Figure 3 are plotted in Figure 5. The output of the inside sensor was 52 nm, which was 210 approximately the same as the command displacement of the diamond tool. The output of the outside 211 sensor was 27 nm. The indentation depth of the reverse cutting edge artifact was calculated to be 25 212 nm by substituting the outputs of two sensors into Equation (5). 213
Figure 4. Copper workpiece. (a) Atomic force microscope (AFM) topography; (b) Roughness of thesection A–A’.
3.1. Effect of Elastic Recovery
The effect of elastic recovery of the reverse cutting edge artifact on cutting edge radius measurementaccuracy was analyzed. An AFM cantilever (OMCL-AC240TS, Olympus, Tokyo, Japan) with a nominaltip radius of 7 nm and a tip height of 14 µm was selected to measure the topographies of the actual andthe reverse diamond tool cutting edge. A single point diamond tool with a nose radius of 1 mm wasmeasured in this test.
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Since the indentation depth and the elastic recovery of the reverse cutting edge artifact are relatedwith each other based on the Hertz theory, a group of reverse cutting edge artifacts with variousindentation depths from 20 to 180 nm were fabricated on the designed nanoindentation system inorder to investigate the effect of the elastic recovery. The interval of indentation depth was set atapproximately 20 nm.
Figure 5 shows the outputs of the inside and the outside sensors when the command displacementof the diamond tool actuated by the FTS was set at 50 nm. Only the outputs in step three of Figure 3are plotted in Figure 5. The output of the inside sensor was 52 nm, which was approximately thesame 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 substitutingthe outputs of two sensors into Equation (5).Appl. Sci. 2020 7 of 14
214 Figure 5. The outputs of the inside and the outside sensors with a command displacement of 50 nm. 215
The diamond tool was positioned on the Z-scanner of the AFM with the bisector of the included 216 angle between its rake face and clearance face. The Olympus AFM cantilever was moved along the 217 X-, Y- and Z-directions by the XY-stage and the Z-scanner of the AFM to make the alignment between 218 the AFM tip and the apex of the diamond tool cutting edge. The actual cutting edge was, then, 219 scanned by the AFM cantilever. The scan range and the scan rate were set to be 2 μm (X) × 2 μm (Y) 220 and 1.2 μm/s, respectively. The numbers of scanning lines in the X- and Y-positions were 1024 and 221 1024, respectively. Figure 6a shows a 3D topography of the diamond tool cutting edge. It can be seen 222 from the figure that there was a clear edge between the rake face and the clearance face, which can 223 be employed for quantitative evaluation of the diamond tool cutting edge radius. The cross-sectional 224 profile extracted from the 3D topography is shown in Figure 6b. The measured tool cutting edge 225 radius was obtained from that of the fitted arc, which was evaluated by fitting the points in the apex 226 of the cross-sectional profile of the cutting edge based on the least square method. The radius of the 227 fitted arc, referred to as Rtool_m, was evaluated to be approximately 40.32 nm. It should be noted that 228 the fitted arc was a geometric convolution of the AFM tip and the actual diamond tool cutting edge. 229 Therefore, the value of 40.32 nm was not the actual diamond tool cutting edge radius. 230
231 Figure 6. Measured diamond tool cutting edge. (a) AFM topography; (b) Profile of Section B–B’. 232
The reverse cutting edge artifact was also placed on the Z-scanner of the AFM. The same AFM 233 cantilever, which had been used to scan the actual cutting edge, was brought to scan the reverse 234 cutting edge. The scanning range, the scan rate, and the number of scanning lines in the X- and Y-235 position were set to be the same as those in the AFM measurement of the actual cutting edge. Figure 236 7a,b shows the AFM topography and the cross-sectional profile of the reverse cutting edge artifact, 237 respectively. It can be seen from Figure 7a that the reverse cutting edge was well transcribed from 238 the geometry of the diamond tool. The depth of the reverse cutting edge artifact was evaluated to be 239 28 nm. It was approximately the same as the indentation depth of 25 nm, which was evaluated based 240 on the outputs of the inside and the outside sensors of the nanoindentation system. The control 241
Out
put o
f ins
ide s
enso
r 1
10 n
m/d
iv.
Out
put o
f out
side
sens
or
50 n
m/d
iv.
Time 5 s/div.
Outside sensor
Inside sensor52 nm
27 nm
X-position 20 nm/div.
Z-po
sitio
n 20
nm
/div.
Rtool_m=40.32 nm
Fitted curve
Raw data
(b)
Figure 5. The outputs of the inside and the outside sensors with a command displacement of 50 nm.
The diamond tool was positioned on the Z-scanner of the AFM with the bisector of the includedangle 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 theAFM tip and the apex of the diamond tool cutting edge. The actual cutting edge was, then, scanned bythe AFM cantilever. The scan range and the scan rate were set to be 2 µm (X) × 2 µm (Y) and 1.2 µm/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 figurethat there was a clear edge between the rake face and the clearance face, which can be employed forquantitative evaluation of the diamond tool cutting edge radius. The cross-sectional profile extractedfrom the 3D topography is shown in Figure 6b. The measured tool cutting edge radius was obtainedfrom that of the fitted arc, which was evaluated by fitting the points in the apex of the cross-sectionalprofile of the cutting edge based on the least square method. The radius of the fitted arc, referred toas Rtool_m, was evaluated to be approximately 40.32 nm. It should be noted that the fitted arc was ageometric convolution of the AFM tip and the actual diamond tool cutting edge. Therefore, the valueof 40.32 nm was not the actual diamond tool cutting edge radius.
Appl. Sci. 2020, 10, 4799 8 of 14
Appl. Sci. 2020 7 of 14
214 Figure 5. The outputs of the inside and the outside sensors with a command displacement of 50 nm. 215
The diamond tool was positioned on the Z-scanner of the AFM with the bisector of the included 216 angle between its rake face and clearance face. The Olympus AFM cantilever was moved along the 217 X-, Y- and Z-directions by the XY-stage and the Z-scanner of the AFM to make the alignment between 218 the AFM tip and the apex of the diamond tool cutting edge. The actual cutting edge was, then, 219 scanned by the AFM cantilever. The scan range and the scan rate were set to be 2 μm (X) × 2 μm (Y) 220 and 1.2 μm/s, respectively. The numbers of scanning lines in the X- and Y-positions were 1024 and 221 1024, respectively. Figure 6a shows a 3D topography of the diamond tool cutting edge. It can be seen 222 from the figure that there was a clear edge between the rake face and the clearance face, which can 223 be employed for quantitative evaluation of the diamond tool cutting edge radius. The cross-sectional 224 profile extracted from the 3D topography is shown in Figure 6b. The measured tool cutting edge 225 radius was obtained from that of the fitted arc, which was evaluated by fitting the points in the apex 226 of the cross-sectional profile of the cutting edge based on the least square method. The radius of the 227 fitted arc, referred to as Rtool_m, was evaluated to be approximately 40.32 nm. It should be noted that 228 the fitted arc was a geometric convolution of the AFM tip and the actual diamond tool cutting edge. 229 Therefore, the value of 40.32 nm was not the actual diamond tool cutting edge radius. 230
231 Figure 6. Measured diamond tool cutting edge. (a) AFM topography; (b) Profile of Section B–B’. 232
The reverse cutting edge artifact was also placed on the Z-scanner of the AFM. The same AFM 233 cantilever, which had been used to scan the actual cutting edge, was brought to scan the reverse 234 cutting edge. The scanning range, the scan rate, and the number of scanning lines in the X- and Y-235 position were set to be the same as those in the AFM measurement of the actual cutting edge. Figure 236 7a,b shows the AFM topography and the cross-sectional profile of the reverse cutting edge artifact, 237 respectively. It can be seen from Figure 7a that the reverse cutting edge was well transcribed from 238 the geometry of the diamond tool. The depth of the reverse cutting edge artifact was evaluated to be 239 28 nm. It was approximately the same as the indentation depth of 25 nm, which was evaluated based 240 on the outputs of the inside and the outside sensors of the nanoindentation system. The control 241
Out
put o
f ins
ide s
enso
r 1
10 n
m/d
iv.
Out
put o
f out
side
sens
or
50 n
m/d
iv.
Time 5 s/div.
Outside sensor
Inside sensor52 nm
27 nm
X-position 20 nm/div.
Z-po
sitio
n 20
nm
/div.
Rtool_m=40.32 nm
Fitted curve
Raw data
(b)
Figure 6. Measured diamond tool cutting edge. (a) AFM topography; (b) Profile of Section B–B’.
The reverse cutting edge artifact was also placed on the Z-scanner of the AFM. The same AFMcantilever, which had been used to scan the actual cutting edge, was brought to scan the reverse cuttingedge. The scanning range, the scan rate, and the number of scanning lines in the X- and Y-positionwere set to be the same as those in the AFM measurement of the actual cutting edge. Figure 7a,b showsthe 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 ofthe diamond tool. The depth of the reverse cutting edge artifact was evaluated to be 28 nm. It wasapproximately the same as the indentation depth of 25 nm, which was evaluated based on the outputsof the inside and the outside sensors of the nanoindentation system. The control accuracy of theindentation depth in the designed nanoindentation system was, therefore, verified from the result.The points in the apex of the measured revered cutting edge were fitted using the least square method,as shown in Figure 7b. The radius of the reverse fitted arc, referred to as Rmark_m, was evaluated to be21.04 nm. Similarly, the reverse fitted arc was a geometric convolution of the AFM tip and the reversecutting edge. The value of 21.04 nm was not the reverse diamond tool cutting edge radius. Assumingξ is equal to zero, the actual cutting edge radius, Rtool, was calculated by substituting the evaluatedRtool_m and Rmark_m into Equation (4) to obtain 30.68 nm. The difference between Rtool and Rtool_m wasevaluated to be 9.64 nm, which was close to the nominal AFM tip radius of 7 nm. On the basis of theexperimental results, the effectiveness of the proposed measurement method for cutting edge radiususing an AFM and a reverse cutting edge artifact was verified.
Appl. Sci. 2020 8 of 14
accuracy of the indentation depth in the designed nanoindentation system was, therefore, verified 242 from the result. The points in the apex of the measured revered cutting edge were fitted using the 243 least square method, as shown in Figure 7b. The radius of the reverse fitted arc, referred to as Rmark_m, 244 was evaluated to be 21.04 nm. Similarly, the reverse fitted arc was a geometric convolution of the 245 AFM tip and the reverse cutting edge. The value of 21.04 nm was not the reverse diamond tool cutting 246 edge radius. Assuming ξ is equal to zero, the actual cutting edge radius, Rtool, was calculated by 247 substituting the evaluated Rtool_m and Rmark_m into Equation (4) to obtain 30.68 nm. The difference 248 between Rtool and Rtool_m was evaluated to be 9.64 nm, which was close to the nominal AFM tip radius 249 of 7 nm. On the basis of the experimental results, the effectiveness of the proposed measurement 250 method for cutting edge radius using an AFM and a reverse cutting edge artifact was verified. 251
252 Figure 7. Measured reverse diamond tool cutting edge. (a) AFM topography; (b) Profile of Section C–253 C’. 254
Rmark_m of other reverse cutting edges with various indentation depths were also evaluated using 255 the proposed measurement method for cutting edge radius. The evaluated Rmark_m and Rtool are plotted 256 in Figure 8. As can be seen in the figure, the average diamond tool cutting edge radius was estimated 257 to be 30.38 nm with a standard deviation of 0.31 nm. Therefore, it was verified that the elastic recovery 258 of the reverse cutting edge artifact did not affect the measurement accuracy of cutting edge radius 259 when the indentation depth was within 20 to 200 nm. 260
261 Figure 8. Experimental results under various indentation depths. 262
In addition, the effect of elastic recovery on measurement uncertainty of cutting edge radius was 263 investigated. The indentation area between the diamond tool cutting edge and the workpiece, shown 264 in Figure 9, can be recognized as a cylinder and a plane surface. According to the Hertz theory [26], 265 for a plane surface and a cylinder with a radius of Rtool, the elastic recovery der of the reverse cutting 266 edge along the X-direction can be expressed by the following equation: 267
Eval
uate
d R
adiu
s nm
0
20
40
60
Rtool_m
Rmark_m
Rtool
Indentation depth nm20 60 100 140 180
Figure 7. Measured reverse diamond tool cutting edge. (a) AFM topography; (b) Profile of Section C–C’.
Rmark_m of other reverse cutting edges with various indentation depths were also evaluated usingthe proposed measurement method for cutting edge radius. The evaluated Rmark_m and Rtool are
Appl. Sci. 2020, 10, 4799 9 of 14
plotted in Figure 8. As can be seen in the figure, the average diamond tool cutting edge radius wasestimated to be 30.38 nm with a standard deviation of 0.31 nm. Therefore, it was verified that theelastic recovery of the reverse cutting edge artifact did not affect the measurement accuracy of cuttingedge radius when the indentation depth was within 20 to 200 nm.
Appl. Sci. 2020 8 of 14
accuracy of the indentation depth in the designed nanoindentation system was, therefore, verified 242 from the result. The points in the apex of the measured revered cutting edge were fitted using the 243 least square method, as shown in Figure 7b. The radius of the reverse fitted arc, referred to as Rmark_m, 244 was evaluated to be 21.04 nm. Similarly, the reverse fitted arc was a geometric convolution of the 245 AFM tip and the reverse cutting edge. The value of 21.04 nm was not the reverse diamond tool cutting 246 edge radius. Assuming ξ is equal to zero, the actual cutting edge radius, Rtool, was calculated by 247 substituting the evaluated Rtool_m and Rmark_m into Equation (4) to obtain 30.68 nm. The difference 248 between Rtool and Rtool_m was evaluated to be 9.64 nm, which was close to the nominal AFM tip radius 249 of 7 nm. On the basis of the experimental results, the effectiveness of the proposed measurement 250 method for cutting edge radius using an AFM and a reverse cutting edge artifact was verified. 251
252 Figure 7. Measured reverse diamond tool cutting edge. (a) AFM topography; (b) Profile of Section C–253 C’. 254
Rmark_m of other reverse cutting edges with various indentation depths were also evaluated using 255 the proposed measurement method for cutting edge radius. The evaluated Rmark_m and Rtool are plotted 256 in Figure 8. As can be seen in the figure, the average diamond tool cutting edge radius was estimated 257 to be 30.38 nm with a standard deviation of 0.31 nm. Therefore, it was verified that the elastic recovery 258 of the reverse cutting edge artifact did not affect the measurement accuracy of cutting edge radius 259 when the indentation depth was within 20 to 200 nm. 260
261 Figure 8. Experimental results under various indentation depths. 262
In addition, the effect of elastic recovery on measurement uncertainty of cutting edge radius was 263 investigated. The indentation area between the diamond tool cutting edge and the workpiece, shown 264 in Figure 9, can be recognized as a cylinder and a plane surface. According to the Hertz theory [26], 265 for a plane surface and a cylinder with a radius of Rtool, the elastic recovery der of the reverse cutting 266 edge along the X-direction can be expressed by the following equation: 267
Eval
uate
d R
adiu
s nm
0
20
40
60
Rtool_m
Rmark_m
Rtool
Indentation depth nm20 60 100 140 180
Figure 8. Experimental results under various indentation depths.
In addition, the effect of elastic recovery on measurement uncertainty of cutting edge radius wasinvestigated. The indentation area between the diamond tool cutting edge and the workpiece, shownin Figure 9, can be recognized as a cylinder and a plane surface. According to the Hertz theory [26],for a plane surface and a cylinder with a radius of Rtool, the elastic recovery der of the reverse cuttingedge along the X-direction can be expressed by the following equation:
der =4π·1L·F·
1− v2
E(6)
where F is the applied indentation force between the diamond tool and the workpiece, which can beobtained from the deflection of the cantilever at the indentation position and the spring constantsof the cantilever in the designed nanoindentation system. L is the length of cylinder, which can beobtained based on the indentation depth and the nose radius of the diamond tool. E and ν representthe Young’s modulus and the Poisson’s ratio of the diamond tool, respectively.
Appl. Sci. 2020 9 of 14
EF
Lder
2114 νπ
−⋅⋅⋅= (6)
where F is the applied indentation force between the diamond tool and the workpiece, which can be 268 obtained from the deflection of the cantilever at the indentation position and the spring constants of 269 the cantilever in the designed nanoindentation system. L is the length of cylinder, which can be 270 obtained based on the indentation depth and the nose radius of the diamond tool. E and ν represent 271 the Young’s modulus and the Poisson’s ratio of the diamond tool, respectively. 272
273 Figure 9. Schematic of the indentation area between the diamond tool and the copper workpiece. 274
Figure 10 shows the elastic recovery of the reverse cutting edge under various indentation 275 depths. The values were employed to evaluate the measurement uncertainty induced by the elastic 276 recovery. The measurement uncertainty of cutting edge radius of a diamond tool with 1 mm nose 277 radius was evaluated based on the Guide to the Uncertainty in Measurement (GUM) [27]. 278
279 Figure 10. The theoretical elastic recovery under various indentation depths. 280
Table 1 shows the calculated uncertainties when the indentation depth was equal to 25 nm. The 281 uncertainty in Rtool_m and Rmark_m was evaluated to be 1.36 and 1.42 nm, respectively. The uncertainty 282 with a coverage factor of k = 2 (95% confidence) in the measurement of the diamond tool cutting edge 283 radius was evaluated to be 1.97 nm, which was smaller than that obtained in our previous research 284 [22]. 285
The measurement uncertainties under various indentation depths are shown in Figure 11. The 286 standard deviation of the evaluated uncertainties was calculated to be 0.005 nm. The results further 287 demonstrated that elastic recovery of the reverse cutting edge did not influence the measurement 288 accuracy of the diamond tool cutting edge radius based on the proposed edge reversal method and 289 the designed nanoindentation system. 290
Table 1. Uncertainty analysis in the measurement of a diamond tool with a nose radius of 1 mm. 291
WorkpieceDiamond
tool
LZ
Y
XFRtool
5
Theo
retic
al e
last
ic re
cove
ry
nm
0.006
0.004
0.002
0
Indentation depth nm20 60 100 140 180
Figure 9. Schematic of the indentation area between the diamond tool and the copper workpiece.
Figure 10 shows the elastic recovery of the reverse cutting edge under various indentation depths.The values were employed to evaluate the measurement uncertainty induced by the elastic recovery.The measurement uncertainty of cutting edge radius of a diamond tool with 1 mm nose radius wasevaluated based on the Guide to the Uncertainty in Measurement (GUM) [27].
Appl. Sci. 2020, 10, 4799 10 of 14
Appl. Sci. 2020 9 of 14
EF
Lder
2114 νπ
−⋅⋅⋅= (6)
where F is the applied indentation force between the diamond tool and the workpiece, which can be 268 obtained from the deflection of the cantilever at the indentation position and the spring constants of 269 the cantilever in the designed nanoindentation system. L is the length of cylinder, which can be 270 obtained based on the indentation depth and the nose radius of the diamond tool. E and ν represent 271 the Young’s modulus and the Poisson’s ratio of the diamond tool, respectively. 272
273 Figure 9. Schematic of the indentation area between the diamond tool and the copper workpiece. 274
Figure 10 shows the elastic recovery of the reverse cutting edge under various indentation 275 depths. The values were employed to evaluate the measurement uncertainty induced by the elastic 276 recovery. The measurement uncertainty of cutting edge radius of a diamond tool with 1 mm nose 277 radius was evaluated based on the Guide to the Uncertainty in Measurement (GUM) [27]. 278
279 Figure 10. The theoretical elastic recovery under various indentation depths. 280
Table 1 shows the calculated uncertainties when the indentation depth was equal to 25 nm. The 281 uncertainty in Rtool_m and Rmark_m was evaluated to be 1.36 and 1.42 nm, respectively. The uncertainty 282 with a coverage factor of k = 2 (95% confidence) in the measurement of the diamond tool cutting edge 283 radius was evaluated to be 1.97 nm, which was smaller than that obtained in our previous research 284 [22]. 285
The measurement uncertainties under various indentation depths are shown in Figure 11. The 286 standard deviation of the evaluated uncertainties was calculated to be 0.005 nm. The results further 287 demonstrated that elastic recovery of the reverse cutting edge did not influence the measurement 288 accuracy of the diamond tool cutting edge radius based on the proposed edge reversal method and 289 the designed nanoindentation system. 290
Table 1. Uncertainty analysis in the measurement of a diamond tool with a nose radius of 1 mm. 291
WorkpieceDiamond
tool
LZ
Y
XFRtool
5
Theo
retic
al e
last
ic re
cove
ry
nm
0.006
0.004
0.002
0
Indentation depth nm20 60 100 140 180
Figure 10. The theoretical elastic recovery under various indentation depths.
Table 1 shows the calculated uncertainties when the indentation depth was equal to 25 nm.The uncertainty in Rtool_m and Rmark_m was evaluated to be 1.36 and 1.42 nm, respectively.The uncertainty with a coverage factor of k = 2 (95% confidence) in the measurement of the diamondtool cutting edge radius was evaluated to be 1.97 nm, which was smaller than that obtained in ourprevious research [22].
The measurement uncertainties under various indentation depths are shown in Figure 11.The standard deviation of the evaluated uncertainties was calculated to be 0.005 nm. The results furtherdemonstrated that elastic recovery of the reverse cutting edge did not influence the measurementaccuracy of the diamond tool cutting edge radius based on the proposed edge reversal method and thedesigned nanoindentation system.
Table 1. Uncertainty analysis in the measurement of a diamond tool with a nose radius of 1 mm.
Uncertainty Sources Symbol Uncertainty Value Distribution Standard Uncertainty
Lateral imaging resolution ur 0.97 nm Rectangular 0.56 nmLateral positioning resolution uL_n 1.2 nm Normal 1.2 nmVertical positioning resolution uV_n 0.2 nm Normal 0.2 nm
Thermal resolution ut_t 3.3 × 10−5 nm Rectangular 1.9 × 10−5 nmMeasurement resolution ut_d 1.457 nm - 0.46 nmUncertainty in Rtool_m utool_m - - 1.36 nm
Lateral imaging resolution ur 0.97 nm Rectangular 0.56 nmLateral positioning resolution uL_n 1.2 nm Normal 1.2 nmVertical positioning resolution uV_n 0.2 nm Normal 0.2 nm
Thermal resolution um_t 4.9 × 10−5 nm Rectangular 2.8 × 10−5 nmMeasurement resolution um_d 0.385 nm - 0.12 nm
Elastic recovery um_e 0.358 nm Rectangular 0.21 nmIndentation force um_f 0.001 nm Rectangular 5.7 × 10−4 nm
Uncertainty in Rmark_m umark_m - - 1.42 nm
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Appl. Sci. 2020 10 of 14
Uncertainty Sources Symbol Uncertainty Value Distribution Standard
Uncertainty Lateral imaging resolution ur 0.97 nm Rectangular 0.56 nm
Lateral positioning resolution
uL_n 1.2 nm Normal 1.2 nm
Vertical positioning resolution
uV_n 0.2 nm Normal 0.2 nm
Thermal resolution ut_t 3.3 × 10−5 nm Rectangular 1.9 × 10−5 nm Measurement resolution ut_d 1.457 nm - 0.46 nm
Uncertainty in Rtool_m utool_m - - 1.36 nm Lateral imaging resolution ur 0.97 nm Rectangular 0.56 nm
Lateral positioning resolution
uL_n 1.2 nm Normal 1.2 nm
Vertical positioning resolution
uV_n 0.2 nm Normal 0.2 nm
Thermal resolution um_t 4.9 × 10−5 nm Rectangular 2.8 × 10−5 nm Measurement resolution um_d 0.385 nm - 0.12 nm
Elastic recovery um_e 0.358 nm Rectangular 0.21 nm Indentation force um_f 0.001 nm Rectangular 5.7 × 10−4 nm
Uncertainty in Rmark_m umark_m - - 1.42 nm
292 Figure 11. The measurement uncertainties of cutting edge radius of a diamond tool under various 293 indentation depths. 294
3.2. Effect of AFM Cantilever Tip 295 The AFM cantilever was one of the crucial factors that affected the evaluation accuracy of the 296
diamond tool cutting edge radius. Therefore, another AFM cantilever (MPP-11100-10, Bruker, 297 Billerica, MA, USA) was installed onto the AFM to scan the actual and the reverse diamond tool 298 cutting edges for investigating the effect of the AFM cantilever tip on the measurement accuracy of 299 the diamond tool cutting edge radius. The Olympus AFM cantilever and the Bruker AFM cantilever 300 were referred to as Cantilever 1 and Cantilever 2, respectively. Differing from Cantilever 1, there was 301 a long base at the top of Cantilever 2. The tip radius of Cantilever 2 was 12 nm, which was larger than 302 that of Cantilever 1. 303
Then, Cantilever 2 was used to scan the actual and the reverse cutting edges, which had been 304 scanned by Cantilever 1. We confirmed that the AFM topographies of the cutting edges scanned by 305 Cantilever 2 were similar to those measured by Cantilever 1, although the AFM images are not shown 306 here for the sake of clarity. Figure 12 shows the measured diamond tool cutting edge radii using 307
Unc
erta
inty
nm
1.90
1.95
2.00
2.05
Indentation depth nm20 60 100 140 180
Figure 11. The measurement uncertainties of cutting edge radius of a diamond tool under variousindentation depths.
3.2. Effect of AFM Cantilever Tip
The AFM cantilever was one of the crucial factors that affected the evaluation accuracy of thediamond tool cutting edge radius. Therefore, another AFM cantilever (MPP-11100-10, Bruker, Billerica,MA, USA) was installed onto the AFM to scan the actual and the reverse diamond tool cutting edgesfor investigating the effect of the AFM cantilever tip on the measurement accuracy of the diamond toolcutting edge radius. The Olympus AFM cantilever and the Bruker AFM cantilever were referred to asCantilever 1 and Cantilever 2, respectively. Differing from Cantilever 1, there was a long base at the topof Cantilever 2. The tip radius of Cantilever 2 was 12 nm, which was larger than that of Cantilever 1.
Then, Cantilever 2 was used to scan the actual and the reverse cutting edges, which had beenscanned by Cantilever 1. We confirmed that the AFM topographies of the cutting edges scannedby Cantilever 2 were similar to those measured by Cantilever 1, although the AFM images are notshown here for the sake of clarity. Figure 12 shows the measured diamond tool cutting edge radiiusing Cantilever 2. The average characterized cutting edge radius of the diamond tool was 29.67 nm,with a standard deviation of 0.16 nm. Characterized cutting edge radius using Cantilever 2 was thesame as that using Cantilever 1. The measurement uncertainty using Cantilever 2 was evaluated.The results are also plotted in Figure 12. The standard deviation of the evaluated uncertainty valueswas calculated to be 0.028 nm. From the above results, it can be seen that the measurement accuracy ofthe diamond tool cutting edge radius based on the proposed edge reversal method was not affected bythe AFM cantilever tip radius. This is consistent with the fact that the effect of the AFM cantilever tipradius can be removed in the proposed method.
Appl. Sci. 2020 11 of 14
Cantilever 2. The average characterized cutting edge radius of the diamond tool was 29.67 nm, with 308 a standard deviation of 0.16 nm. Characterized cutting edge radius using Cantilever 2 was the same 309 as that using Cantilever 1. The measurement uncertainty using Cantilever 2 was evaluated. The 310 results are also plotted in Figure 12. The standard deviation of the evaluated uncertainty values was 311 calculated to be 0.028 nm. From the above results, it can be seen that the measurement accuracy of 312 the diamond tool cutting edge radius based on the proposed edge reversal method was not affected 313 by the AFM cantilever tip radius. This is consistent with the fact that the effect of the AFM cantilever 314 tip radius can be removed in the proposed method. 315
316 Figure 12. Experimental results using Cantilever 2. 317
3.3. Reliability of the Proposed Method and the Designed System 318 To further demonstrate the reliability of the proposed measurement method, cutting edge radius 319
of a diamond tool with a different nose radius of 2 mm, which was referred to as Diamond Tool 2, 320 was also evaluated. 321
Diamond Tool 2 was mounted on the nanoindentation system to replicate its cutting edge on the 322 copper workpiece with various indentation depths. The AFM with Cantilever 1 was, then, applied to 323 measure the profiles of the actual and replicated cutting edges. The command displacement of 324 Diamond Tool 2 actuated by the FTS was also set from 50 to 300 nm with an interval of 50 nm. 325 However, the corresponding indentation depths were evaluated to be 35, 45, 77, 104, 127, and 163 nm 326 according to the outputs of the inside and the outside sensors, which were different from those by 327 the previous diamond tool with a nose radius of 1 mm. 328
The measured results of Diamond Tool 2 are summarized in Figure 13. The average radius of 329 the diamond tool cutting edge was evaluated to be 41.29 nm with a standard deviation of 0.66 nm. 330 The standard deviation of the evaluated uncertainty values was calculated to be 0.032 nm. The 331 difference between the actual cutting edge radius by the proposed measurement method (Rtool) and 332 the cutting edge radius imaged directly by the AFM (Rtool_m) of Diamond Tool 2 was evaluated to be 333 7.36 nm. This value was also close to the nominal AFM tip radius of 7 nm. The reliability of the 334 proposed method was, thus, verified from the measurement results of Diamond Tool 2. 335
Uncertainty
The
actu
al c
uttin
g ed
ge ra
dius
nm
33
27
29
31
Unc
erta
inty
nm
Cutting edge radius2.15
1.85
1.95
2.05
Indentation depth nm20 60 100 140 180
Figure 12. Experimental results using Cantilever 2.
Appl. Sci. 2020, 10, 4799 12 of 14
3.3. Reliability of the Proposed Method and the Designed System
To further demonstrate the reliability of the proposed measurement method, cutting edge radiusof a diamond tool with a different nose radius of 2 mm, which was referred to as Diamond Tool 2,was also evaluated.
Diamond Tool 2 was mounted on the nanoindentation system to replicate its cutting edge on thecopper workpiece with various indentation depths. The AFM with Cantilever 1 was, then, appliedto measure the profiles of the actual and replicated cutting edges. The command displacement ofDiamond Tool 2 actuated by the FTS was also set from 50 to 300 nm with an interval of 50 nm. However,the corresponding indentation depths were evaluated to be 35, 45, 77, 104, 127, and 163 nm accordingto the outputs of the inside and the outside sensors, which were different from those by the previousdiamond tool with a nose radius of 1 mm.
The measured results of Diamond Tool 2 are summarized in Figure 13. The average radius ofthe diamond tool cutting edge was evaluated to be 41.29 nm with a standard deviation of 0.66 nm.The standard deviation of the evaluated uncertainty values was calculated to be 0.032 nm. The differencebetween the actual cutting edge radius by the proposed measurement method (Rtool) and the cuttingedge radius imaged directly by the AFM (Rtool_m) of Diamond Tool 2 was evaluated to be 7.36 nm.This value was also close to the nominal AFM tip radius of 7 nm. The reliability of the proposedmethod was, thus, verified from the measurement results of Diamond Tool 2.Appl. Sci. 2020 12 of 14
336 Figure 13. Experimental results of measuring Diamond Tool 2. 337
4. Summary 338 In this paper, we presented high-precision cutting edge radius measurement of single point 339
diamond tools using an atomic force microscope and a reverse cutting edge artifact based on the edge 340 reversal method. A reverse cutting-edge artifact with a high-precision depth was fabricated on a 341 workpiece surface using the optimized operation of a newly designed nanoindentation system. 342 Cutting edge radius was evaluated from two AFM images, including an AFM image of the actual 343 cutting edge and an AFM image of the reverse cutting edge, from which the convolution effect of the 344 AFM tip radius was reduced. Cutting edge radii of two diamond tools were evaluated. The first tool 345 had a nose radius of 1 mm and the second tool had a nose radius of 2 mm. The difference between 346 cutting edge radii evaluated by the proposed measurement method and that directly obtained from 347 the AFM image was 9.64 nm for the first tool and 7.36 nm for the second tool. Both values were close 348 to the AFM probe tip nominal radius of 7 nm, from which the feasibility and the reliability of the 349 proposed method were demonstrated. The effect of the elastic recovery was investigated by scanning 350 a group of reverse cutting edge artifacts with various depths from 20 to 180 nm. We confirmed that 351 the elastic recovery of the reverse cutting edge did not affect the measurement accuracy of cutting 352 edge radius when the indentation depth was within 20 to 200 nm. Three-dimensional profile 353 measurements of diamond tool cutting edge based on the proposed measurement method will be 354 carried out in the future work. 355 Author Contributions: Conceptualization, W.G., Y.S., and Y.C., Data curation, K.Z. and H.M.; Formal analysis, 356 K.Z. and Y.C.; Investigation, Y.S. and Y.C.; Methodology, W.G.; Supervision, W.G.; Visualization, H.M.; 357 Writing—original draft, K.Z.; Writing—review and editing, W.G and Y.C. 358 Funding: This research is supported by a Japanese Government (MEXT) Scholarship. K.Z. thanks the support 359 from the China Scholarship Council (CSC). In addition, a part of this research is supported by the Japan Society 360 for the Promotion of Science (JSPS) 15H05759 and 20H00211. 361 Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the 362 study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision 363 to publish the results. 364
References 365 1. Zhu, Z.W.; To, S.; Zhang, S.J. Large-scale Fabrication of micro-lens array by novel end-fly-cutting servo 366
diamond machining. Opt. Express 2015, 23, 20593–20604. 367 2. Gong, H.; Wang, Y.; Song, L.; Fang, F.Z. Spiral tool path generation for diamond turning optical freeform 368
surfaces of quasi-revolution. Comput. Aided Des. 2015, 59, 15–22. 369 3. Gao, W.; Araki, T.; Kiyono, S.; Okazaki, Y.; Yamanaka, M. Precision nano-fabrication and evaluation of a 370
large area sinusoidal grid surface for a surface encoder. Precis. Eng. 2003, 27, 289–298. 371
Uncertainty
The
actu
al c
uttin
g ed
ge ra
dius
nm
44
38
40
42
Unc
erta
inty
nm
Cutting edge radius2.15
1.85
1.95
2.05
Indentation depth nm20 60 100 140 180
Figure 13. Experimental results of measuring Diamond Tool 2.
4. Summary
In this paper, we presented high-precision cutting edge radius measurement of single pointdiamond tools using an atomic force microscope and a reverse cutting edge artifact based on theedge reversal method. A reverse cutting-edge artifact with a high-precision depth was fabricatedon a workpiece surface using the optimized operation of a newly designed nanoindentation system.Cutting edge radius was evaluated from two AFM images, including an AFM image of the actualcutting edge and an AFM image of the reverse cutting edge, from which the convolution effect of theAFM tip radius was reduced. Cutting edge radii of two diamond tools were evaluated. The first toolhad a nose radius of 1 mm and the second tool had a nose radius of 2 mm. The difference betweencutting edge radii evaluated by the proposed measurement method and that directly obtained fromthe AFM image was 9.64 nm for the first tool and 7.36 nm for the second tool. Both values were closeto the AFM probe tip nominal radius of 7 nm, from which the feasibility and the reliability of theproposed method were demonstrated. The effect of the elastic recovery was investigated by scanning agroup of reverse cutting edge artifacts with various depths from 20 to 180 nm. We confirmed that theelastic recovery of the reverse cutting edge did not affect the measurement accuracy of cutting edgeradius when the indentation depth was within 20 to 200 nm. Three-dimensional profile measurements
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of diamond tool cutting edge based on the proposed measurement method will be carried out in thefuture work.
Author Contributions: Conceptualization, W.G., Y.S., and Y.C., Data curation, K.Z. and H.M.; Formal analysis, K.Z.and Y.C.; Investigation, Y.S. and Y.C.; Methodology, W.G.; Supervision, W.G.; Visualization, H.M.; Writing—originaldraft, K.Z.; Writing—review and editing, W.G. and Y.C. All authors have read and agreed to the published versionof the manuscript.
Funding: This research is supported by a Japanese Government (MEXT) Scholarship. K.Z. thanks the supportfrom the China Scholarship Council (CSC). In addition, a part of this research is supported by the Japan Societyfor the Promotion of Science (JSPS) 15H05759 and 20H00211.
Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of thestudy; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision topublish the results.
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