Figure 1.
The mathematical model of the flank surface of the helical point micro-drill.
Figure 1.
The mathematical model of the flank surface of the helical point micro-drill.
Figure 2.
The mathematical model of the micro-drill flute.
Figure 2.
The mathematical model of the micro-drill flute.
Figure 3.
Dynamic rake angle distribution along the chisel edge with n = 14,000 r/min, f = 0.003 mm/r: (a) point angle; (b) helix angle; (c) web thickness ratio.
Figure 3.
Dynamic rake angle distribution along the chisel edge with n = 14,000 r/min, f = 0.003 mm/r: (a) point angle; (b) helix angle; (c) web thickness ratio.
Figure 4.
Dynamic rake angle distribution along the cutting lip with n = 14,000 r/min, f = 0.003 mm/r: (a) point angle; (b) helix angle; and (c) web thickness ratio.
Figure 4.
Dynamic rake angle distribution along the cutting lip with n = 14,000 r/min, f = 0.003 mm/r: (a) point angle; (b) helix angle; and (c) web thickness ratio.
Figure 5.
The shape of the cutting lip: (a) point angle; and (b) helix angle.
Figure 5.
The shape of the cutting lip: (a) point angle; and (b) helix angle.
Figure 6.
The uncut chip thickness along the cutting lip with n = 14,000 r/min, f = 0.003 mm/r: (a) point angle; and (b) helix angle.
Figure 6.
The uncut chip thickness along the cutting lip with n = 14,000 r/min, f = 0.003 mm/r: (a) point angle; and (b) helix angle.
Figure 7.
The six-axis CNC grinding machine.
Figure 7.
The six-axis CNC grinding machine.
Figure 8.
The geometry and configuration of the grinding wheels.
Figure 8.
The geometry and configuration of the grinding wheels.
Figure 9.
The structure of the micro-drill.
Figure 9.
The structure of the micro-drill.
Figure 10.
The fabricated result of helical point micro-drills. (a) ρ = 59°, β = 30°, 2t/d = 0.25; and (b) ρ = 65°, β = 40°, 2t/d = 0.3; (c) ρ = 70°, β = 20°, 2t/d = 0.25.
Figure 10.
The fabricated result of helical point micro-drills. (a) ρ = 59°, β = 30°, 2t/d = 0.25; and (b) ρ = 65°, β = 40°, 2t/d = 0.3; (c) ρ = 70°, β = 20°, 2t/d = 0.25.
Figure 11.
The drilling experiment setup on a DMG machining center.
Figure 11.
The drilling experiment setup on a DMG machining center.
Figure 12.
Schematic diagram of burr height measurement and the 2D box-counting method. (a) The burr height measurement (b) the 2D box-counting method.
Figure 12.
Schematic diagram of burr height measurement and the 2D box-counting method. (a) The burr height measurement (b) the 2D box-counting method.
Figure 13.
Thrust force of micro-drills with different geometric parameters. (a) ρ = 59°, β = 40°, 2t/d = 0.25; (b) ρ = 65°, β = 20°, 2t/d = 0.25; (c) ρ = 70°, β = 30°, 2t/d = 0.3.
Figure 13.
Thrust force of micro-drills with different geometric parameters. (a) ρ = 59°, β = 40°, 2t/d = 0.25; (b) ρ = 65°, β = 20°, 2t/d = 0.25; (c) ρ = 70°, β = 30°, 2t/d = 0.3.
Figure 14.
Main effect plot for mean of thrust force: (a) point angle; (b) helical angle; (c) web thickness.
Figure 14.
Main effect plot for mean of thrust force: (a) point angle; (b) helical angle; (c) web thickness.
Figure 15.
Entrance burr for helical point micro-drills with different geometric parameters. (a) ρ = 59°, β = 20°, 2t/d = 0.3; and (b) ρ = 65°, β = 30°, 2t/d = 0.25; (c) ρ = 70°, β = 40°, 2t/d = 0.25.
Figure 15.
Entrance burr for helical point micro-drills with different geometric parameters. (a) ρ = 59°, β = 20°, 2t/d = 0.3; and (b) ρ = 65°, β = 30°, 2t/d = 0.25; (c) ρ = 70°, β = 40°, 2t/d = 0.25.
Figure 16.
Exit burr for helical point micro-drills with different geometric parameters. (a) ρ = 59°, β = 20°, 2t/d = 0.3; and (b) ρ = 65°, β = 20°, 2t/d = 0.25; (c) ρ = 70°, β = 30°, 2t/d = 0.3.
Figure 16.
Exit burr for helical point micro-drills with different geometric parameters. (a) ρ = 59°, β = 20°, 2t/d = 0.3; and (b) ρ = 65°, β = 20°, 2t/d = 0.25; (c) ρ = 70°, β = 30°, 2t/d = 0.3.
Figure 17.
Main effects plot for the mean of the exit burr height: (a) point angle; (b) helical angle; (c) web thickness.
Figure 17.
Main effects plot for the mean of the exit burr height: (a) point angle; (b) helical angle; (c) web thickness.
Figure 18.
Main effects plot for the mean of the entrance burr height: (a) point angle; (b) helical angle; (c) web thickness.
Figure 18.
Main effects plot for the mean of the entrance burr height: (a) point angle; (b) helical angle; (c) web thickness.
Figure 19.
The hole wall morphology. (a) The hole wall morphology; (b) the 3D laser scanning morphology; (c) the hole wall profile.
Figure 19.
The hole wall morphology. (a) The hole wall morphology; (b) the 3D laser scanning morphology; (c) the hole wall profile.
Figure 20.
Main effects plot for the mean of the fractal dimension: (a) point angle; (b) helical angle; (c) web thickness.
Figure 20.
Main effects plot for the mean of the fractal dimension: (a) point angle; (b) helical angle; (c) web thickness.
Table 1.
The geometric parameters of the micro-drill.
Table 1.
The geometric parameters of the micro-drill.
Parameters | Value |
---|
Drill Diameters d (mm) | 0.5 |
Web Thickness Ratio | 0.2, 0.25, 0.3, 0.35, 0.4 |
Helix Angle of the Flute β0 (°) | 20, 25, 30, 35, 40 |
Semi-Point Angle ρ (°) | 50, 55, 59, 65, 70 |
Chisel Edge Angle ψ (°) | 55 |
Lip Clearance Angle αfc (°) | 12 |
Heel Clearance Angle (°) | 15 |
Table 2.
The wheel profile and position parameters.
Table 2.
The wheel profile and position parameters.
Parameters | Value |
---|
Installation Angle λ (°) | 60 |
Distance ax (mm) | 67.5625 |
Wheel Radius R0 (mm) | 67.5 |
Wheel Thickness u1 (mm) | 4 |
Wheel Inclined Angle η (°) | 45 |
Table 3.
The factor level table of micro drill geometry parameters.
Table 3.
The factor level table of micro drill geometry parameters.
Level | Semi-Point Angle ρ (°) | Web Thickness Ratio 2t/d | Helix Angle β0 (°) |
---|
1 | 59 | 0.25d | 20 |
2 | 65 | 0.3d | 30 |
3 | 70 | - | 40 |
Table 4.
Geometric parameters of helical point micro-drills.
Table 4.
Geometric parameters of helical point micro-drills.
No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|
Semi-point angle ρ (°) | 59 | 59 | 59 | 65 | 65 | 65 | 70 | 70 | 70 |
Helix angle β0 (°) | 20 | 30 | 40 | 20 | 30 | 40 | 20 | 30 | 40 |
Web thickness 2t (mm) | 0.15 | 0.125 | 0.125 | 0.125 | 0.125 | 0.15 | 0.125 | 0.15 | 0.125 |
Drill diameter d (mm) | 0.5 | Drill shank diameter ds (mm) | 3 | Drill neck angle αn (°) | 10 |
Flute length L (mm) | 1.5 | Drill whole length Ls (mm) | 50 | Length of the drill overhang out of the tool holder L0 (mm) | 12 |
Table 5.
Thrust force, burr heights, and hole wall quality with different drill geometry parameters.
Table 5.
Thrust force, burr heights, and hole wall quality with different drill geometry parameters.
No. | ρ (°) | β (°) | 2t (mm) | Thrust Force (N) | Henter (μm) | Hexit (μm) | Fractal Dimension DL |
---|
1 | 59 | 20 | 0.150 | 16.44 | 58.10 | 52.02 | 1.51179 |
2 | 59 | 30 | 0.125 | 14.53 | 56.87 | 46.48 | 1.55892 |
3 | 59 | 40 | 0.125 | 12.88 | 35.99 | 36.95 | 1.55841 |
4 | 65 | 20 | 0.125 | 16.94 | 43.57 | 33.30 | 1.54190 |
5 | 65 | 30 | 0.125 | 15.85 | 42.38 | 28.93 | 1.54540 |
6 | 65 | 40 | 0.150 | 17.53 | 30.79 | 24.13 | 1.54188 |
7 | 70 | 20 | 0.125 | 18.83 | 68.13 | 28.91 | 1.56302 |
8 | 70 | 30 | 0.150 | 19.12 | 74.96 | 33.68 | 1.55019 |
9 | 70 | 40 | 0.125 | 17.88 | 60.67 | 20.32 | 1.58085 |
Table 6.
The range analysis results with different drill geometry parameters.
Table 6.
The range analysis results with different drill geometry parameters.
Geometry Parameters | Level | Thrust Force (N) | Henter (μm) | Hexit (μm) | Fractal Dimension DL |
---|
Semi-point angle ρ | Level 1 | 14.62 | 50.32 | 45.15 | 1.543039 |
Level 2 | 16.77 | 38.91 | 28.79 | 1.54306 |
Level 3 | 18.61 | 67.92 | 27.64 | 1.564687 |
Range | 3.99 | 29.01 | 17.51 | 0.021647 |
Helix angle β | Level 1 | 17.40 | 56.60 | 38.08 | 1.538903 |
Level 2 | 16.50 | 58.07 | 36.36 | 1.551503 |
Level 3 | 16.10 | 42.48 | 27.13 | 1.56038 |
Range | 1.31 | 15.59 | 10.94 | 0.021477 |
Web thickness 2t | Level 1 | 16.15 | 51.27 | 32.48 | 1.558083 |
Level 2 | 17.70 | 54.62 | 36.61 | 1.534619 |
Range | 1.55 | 3.35 | 4.13 | 0.023464 |
Table 7.
ANOVA results for thrust force.
Table 7.
ANOVA results for thrust force.
Source of Variance | DF | Seq SS | Adj SS | Adj MS | F | F-Test * |
---|
Semi-point angle | 2 | 23.9502 | 23.9502 | 11.9751 | 30.4 | 9.55 |
Helix angle | 2 | 2.6866 | 2.6866 | 1.3433 | 1.3433 | 9.55 |
Web thickness | 1 | 4.7749 | 4.7749 | 4.7749 | 12.15 | 10.1 |
Error | 3 | 1.1788 | 1.1788 | 0.3929 | - | - |
Total | 8 | 32.5906 | - | - | - | - |
Table 8.
ANOVA results for the exit burr height.
Table 8.
ANOVA results for the exit burr height.
Source of Variance | DF | Seq SS | Adj SS | Adj MS | F | F-Test * |
---|
Semi-point angle | 2 | 575.76 | 575.76 | 287.88 | 108.07 | 9.55 |
Helix angle | 2 | 207.87 | 207.87 | 103.93 | 39.02 | 9.55 |
Web thickness | 1 | 34.05 | 34.05 | 34.05 | 12.78 | 10.1 |
Error | 3 | 7.99 | 7.99 | 2.66 | - | - |
Total | 8 | 825.66 | - | - | - | - |
Table 9.
ANOVA results for the entrance burr height.
Table 9.
ANOVA results for the entrance burr height.
Source of Variance | DF | Seq SS | Adj SS | Adj MS | F | F-Test * |
---|
Semi-point angle | 2 | 1281.11 | 1281.11 | 640.56 | 43.94 | 9.55 |
Helix angle | 2 | 444.28 | 444.28 | 222.14 | 15.24 | 9.55 |
Web thickness | 1 | 22.41 | 22.41 | 22.41 | 1.54 | 10.1 |
Error | 3 | 43.74 | 43.74 | 14.58 | - | - |
Total | 8 | 1791.55 | - | - | - | - |
Table 10.
ANOVA results for the fractal dimension.
Table 10.
ANOVA results for the fractal dimension.
Source of Variance | DF | Seq SS | Adj SS | Adj MS | F | F-Test * |
---|
Semi-point angle | 2 | 0.0009363 | 0.0009363 | 0.0004682 | 9.52 | 9.55 |
Helix angle | 2 | 0.0006989 | 0.0006989 | 0.0003494 | 7.11 | 9.55 |
Web thickness | 1 | 0.0011011 | 0.0011011 | 0.0011011 | 22.39 | 10.1 |
Error | 3 | 0.0001475 | 0.0001475 | 0.0000492 | - | - |
Total | 8 | 0.0028838 | - | - | - | - |