Author Contributions
Conceptualization, Y.-T.L., J.-L.J. and D.-M.T.; methodology, Y.-T.L., J.-L.J., M.S., D.-M.T., G.-S.H. and B.-J.L.; software, Y.-T.L. and J.-L.J.; validation, Y.-T.L., J.-L.J., M.S., D.-M.T., G.-S.H. and B.-J.L.; formal analysis, Y.-T.L. and J.-L.J.; investigation, Y.-T.L. and J.-L.J.; resources, M.S. and B.-J.L.; data curation, Y.-T.L. and J.-L.J.; writing—original draft preparation, Y.-T.L., J.-L.J. and G.-S.H.; writing—review and editing, G.-S.H.; visualization, Y.-T.L., J.-L.J. and G.-S.H.; supervision, D.-M.T.; project administration, D.-M.T.; funding acquisition, D.-M.T. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Cutting area intersected by tooth paths and scroll workpiece: (a) full view, (b) zoomed-in view.
Figure 1.
Cutting area intersected by tooth paths and scroll workpiece: (a) full view, (b) zoomed-in view.
Figure 2.
Stability lobes and multiple factor K.
Figure 2.
Stability lobes and multiple factor K.
Figure 3.
Flowchart of chatter suppression program.
Figure 3.
Flowchart of chatter suppression program.
Figure 4.
Operation interface for chatter suppression program: (a) microphone audio frequency in the time domain, (b) FFT spectrum of the audio frequency, (c) frequency information and current spindle speed, (d) machining information and conditions.
Figure 4.
Operation interface for chatter suppression program: (a) microphone audio frequency in the time domain, (b) FFT spectrum of the audio frequency, (c) frequency information and current spindle speed, (d) machining information and conditions.
Figure 5.
Procedures of the Taguchi method.
Figure 5.
Procedures of the Taguchi method.
Figure 6.
Tongtai TMV-720A vertical milling machine.
Figure 6.
Tongtai TMV-720A vertical milling machine.
Figure 7.
Tool holder embedded with sensors (Spike® from Pro-micron GmbH).
Figure 7.
Tool holder embedded with sensors (Spike® from Pro-micron GmbH).
Figure 8.
Cutting area per cutter tooth in the rough machining process.
Figure 8.
Cutting area per cutter tooth in the rough machining process.
Figure 9.
Variation in feed rate for different cutting areas per cutter tooth.
Figure 9.
Variation in feed rate for different cutting areas per cutter tooth.
Figure 10.
Variation in bending moments with a constant feed rate of 800 mm/min.
Figure 10.
Variation in bending moments with a constant feed rate of 800 mm/min.
Figure 11.
Maximum bending moments with different feed rate limits and adaptive feed rate planning.
Figure 11.
Maximum bending moments with different feed rate limits and adaptive feed rate planning.
Figure 12.
Material removal rates with different feed rate limits and adaptive feed rate planning.
Figure 12.
Material removal rates with different feed rate limits and adaptive feed rate planning.
Figure 13.
Scroll workpiece after the rough machining processes.
Figure 13.
Scroll workpiece after the rough machining processes.
Figure 14.
Experimental results displayed in the operation interface of the developed program: (a) S = 5000 rpm, (b) S = 6879 rpm.
Figure 14.
Experimental results displayed in the operation interface of the developed program: (a) S = 5000 rpm, (b) S = 6879 rpm.
Figure 15.
Effects of chatter suppression.
Figure 15.
Effects of chatter suppression.
Figure 16.
Measurement of the profile errors for scrolls.
Figure 16.
Measurement of the profile errors for scrolls.
Figure 17.
Measurement of the surface roughness of scrolls.
Figure 17.
Measurement of the surface roughness of scrolls.
Figure 18.
Graph of S/N ratios for profile errors.
Figure 18.
Graph of S/N ratios for profile errors.
Figure 19.
Graph of mean values for profile errors.
Figure 19.
Graph of mean values for profile errors.
Figure 20.
Graph of S/N ratios for surface roughness.
Figure 20.
Graph of S/N ratios for surface roughness.
Figure 21.
Graph of mean values for surface roughness.
Figure 21.
Graph of mean values for surface roughness.
Figure 22.
Scroll workpiece after the fine machining processes.
Figure 22.
Scroll workpiece after the fine machining processes.
Table 1.
Specifications of the Starpoint S2009 cutter.
Table 1.
Specifications of the Starpoint S2009 cutter.
Tooth Diameter (mm) | Tooth Length (mm) | Cutter Length (mm) | Handle Diameter (mm) |
---|
12 | 50 | 100 | 12 |
Tooth | Tool appearance | |
2 |
Table 2.
Specifications of the tool holder.
Table 2.
Specifications of the tool holder.
Signal Reception | Wireless 2.45 GHz |
Sampling Rate | 1800 Hz |
Measuring Range | Tension | ±37.2 kN |
Bending Moment | ±462.6 Nm |
Torque | ±584.0 Nm |
Table 3.
Experimental results without and with adaptive feed rate planning.
Table 3.
Experimental results without and with adaptive feed rate planning.
Cutting Area per Cutter Tooth Az (mm2) | Feed Rate Limit (mm/min) | Maximum Bending Moment (Nm) | Machining Time (s) | Material Removal Rate (mm3/s) |
---|
Without adaptive feed rate planning | 700 | 26.04 | 55.82 | 160.41 |
800 | 26.84 | 48.83 | 183.35 |
900 | 28.11 | 43.17 | 207.38 |
1000 | 29.80 | 39.48 | 226.78 |
1100 | 31.27 | 35.54 | 251.91 |
1200 | 33.12 | 32.97 | 271.53 |
0.4 | 700 | 23.74 | 62.16 | 144.03 |
800 | 24.38 | 53.13 | 168.50 |
900 | 25.88 | 50.37 | 177.75 |
1000 | 27.14 | 46.79 | 191.34 |
1100 | 28.58 | 45.04 | 198.77 |
1200 | 31.91 | 43.33 | 206.61 |
0.5 | 700 | 22.72 | 55.92 | 160.11 |
800 | 24.46 | 49.86 | 179.55 |
900 | 25.34 | 46.12 | 194.12 |
1000 | 26.62 | 42.69 | 209.74 |
1100 | 28.89 | 41.05 | 218.12 |
1200 | 29.96 | 38.40 | 233.15 |
0.6 | 700 | 26.06 | 56.90 | 157.35 |
800 | 28.24 | 50.02 | 178.98 |
900 | 30.09 | 44.44 | 201.47 |
1000 | 33.02 | 41.51 | 215.71 |
1100 | 34.74 | 38.68 | 231.49 |
1200 | 35.78 | 36.49 | 245.36 |
Table 4.
Specifications of the Nachi LIST 6212 cutter and the machining parameters.
Table 4.
Specifications of the Nachi LIST 6212 cutter and the machining parameters.
Tooth Diameter ϕDc (mm) | Tooth Length L (mm) | Tool Length L (mm) | Handle Diameter ϕDs (mm) | Cutter Tooth |
---|
6 | 25 | 65 | 8 | 4 |
Tool Appearance | |
Machining Parameters | Spindle Speed S (rpm) | Cutting Depth (mm) | Cutting Width (mm) | Chatter Frequency (Hz) |
5000 | 6 | 0.2 | 2293 |
Table 5.
Results of the chatter suppression tests.
Table 5.
Results of the chatter suppression tests.
Spindle Speed S (rpm) | Multiple Factor K | Maximum Amplitude | Chatter |
---|
5000 | 6.879 | 81.83 | Yes |
4299 | 8 | 29.92 | No |
4914 | 7 | 40.49 | No |
5733 | 6 | 38.13 | No |
6879 | 5 | 24.14 | No |
4046 | 8.5 | 61.54 | Yes |
4586 | 7.5 | 32.92 | Yes |
5292 | 6.5 | 82.72 | Yes |
6254 | 5.5 | 65.05 | Yes |
Table 6.
Specifications of the 7 leaders E143-8 cutter.
Table 6.
Specifications of the 7 leaders E143-8 cutter.
Tooth Diameter (mm) | Tooth Length (mm) | Cutter Length (mm) | Handle Diameter (mm) | Tooth |
---|
8 | 20 | 60 | 8 | 3 |
Tool Appearance | |
Table 7.
Factors and levels used in the experiments.
Table 7.
Factors and levels used in the experiments.
Milling Parameters | Symbol | Level |
---|
1 | 2 | 3 |
---|
Spindle speed (rpm) | A | 10,000 | 15,000 | 20,000 |
Feed rate (mm/min) | B | 500 | 1000 | 1500 |
Tool path | C | Linear (G01) | B-spline | Four-axis concurrency |
Table 8.
Orthogonal array of the experimental factors and levels.
Table 8.
Orthogonal array of the experimental factors and levels.
Experiment Number | Factors and Levels |
---|
Spindle Speed (rpm), A | Feed Rate (mm/min), B | Tool Path, C |
---|
1 (A1B1C1) | 10,000 | 500 | Linear (G01) |
2 (A1B2C2) | 10,000 | 1000 | B-spline |
3 (A1B3C3) | 10,000 | 1500 | Four-axis concurrency |
4 (A2B1C2) | 15,000 | 500 | B-spline |
5 (A2B2C3) | 15,000 | 1000 | Four-axis concurrency |
6 (A2B3C1) | 15,000 | 1500 | Linear (G01) |
7 (A3B1C3) | 20,000 | 500 | Four-axis concurrency |
8 (A3B2C1) | 20,000 | 1000 | Linear (G01) |
9 (A3B3C2) | 20,000 | 1500 | B-spline |
Table 9.
Measured values, means, and S/N ratios of profile errors.
Table 9.
Measured values, means, and S/N ratios of profile errors.
Experiment Number | Measured Values of Profile Errors yi (μm) | Mean (μm) | S/N Ratio ηj (dB) |
---|
1 (A1B1C1) | 3.1 | 2.8 | 2.6 | 1.5 | 3.5 | 3.6 | 8.4 | 7.7 | 4.15 | 46.44 |
2 (A1B2C2) | 1.7 | 4.6 | 3.3 | 5.7 | 3.7 | 4.8 | 16.4 | 13.6 | 6.73 | 41.56 |
3 (A1B3C3) | 2.3 | 3.3 | 7.9 | 3.6 | 3.2 | 3.0 | 11.6 | 57.7 | 11.29 | 33.51 |
4 (A2B1C2) | 1.2 | 2.2 | 3.5 | 0.5 | 0.8 | 2.9 | 10.3 | 2.7 | 3.01 | 47.53 |
5 (A2B2C3) | 1.0 | 3.3 | 2.1 | 7.9 | 1.6 | 3.8 | 11.9 | 59.1 | 11.34 | 33.31 |
6 (A2B3C1) | 12.0 | 2.8 | 7.1 | 2.4 | 4.9 | 9.5 | 31.5 | 33.1 | 12.91 | 35.21 |
7 (A3B1C3) | 3.6 | 0.6 | 4.6 | 5.6 | 5.9 | 1.7 | 11.7 | 50.9 | 10.58 | 34.51 |
8 (A3B2C1) | 2.0 | 0.3 | 1.1 | 2.0 | 2.5 | 3.4 | 17.5 | 10.7 | 4.94 | 42.52 |
9 (A3B3C2) | 0.8 | 7.5 | 1.0 | 4.9 | 3.4 | 6.9 | 37.0 | 24.7 | 10.78 | 35.77 |
Table 10.
Response table for S/N ratios for profile errors.
Table 10.
Response table for S/N ratios for profile errors.
| Factor | A (Spindle Speed) | B (Feed Rate) | C (Tool Path) |
---|
Level | |
---|
1 | | 40.51 | 42.83 | 41.39 |
2 | | 38.69 | 39.13 | 41.62 |
3 | | 37.60 | 34.83 | 33.78 |
Δmax−min | | 2.91 | 8.00 | 7.84 |
Rank | | 3 | 1 | 2 |
Table 11.
Response table for mean values for profile errors.
Table 11.
Response table for mean values for profile errors.
| Factor | A (Spindle Speed) | B (Feed Rate) | C (Tool Path) |
---|
Level | |
---|
1 | | 0.007388 | 0.005913 | 0.007333 |
2 | | 0.009088 | 0.007667 | 0.006837 |
3 | | 0.008763 | 0.011658 | 0.011067 |
Δmax−min | | 0.001700 | 0.005746 | 0.004229 |
Rank | | 3 | 1 | 2 |
Table 12.
ANOVA for the profile errors.
Table 12.
ANOVA for the profile errors.
Factor | Degree of Freedom (DF) | Sum of Squares (SS) | Mean Square (MS) | F-Ratio (FX) | Contribution (PX) |
---|
A (spindle speed) | 2 | 12.94 | 6.47 | 0.67 | -- |
B (feed rate) | 2 | 96.16 | 48.08 | 4.95 | 30.5% |
C (tool path) | 2 | 119.51 | 59.76 | 6.15 | 39.7% |
Error | 2 | 25.92 | 12.96 | | |
Total | 8 | 254.53 | | | |
Pooled error | 4 | 38.86 | 9.72 | | |
Table 13.
Measured values, means, and S/N ratios of profile errors from verification experiments.
Table 13.
Measured values, means, and S/N ratios of profile errors from verification experiments.
Experiment Number | Measured y Value (μm) | Mean (μm) | S/N Ratio η (dB) |
---|
1 | 2.4 | 3.6 | 6.1 | 8.2 | 2.8 | 2.4 | 12.1 | 9.1 | 5.84 | 43.40 |
2 | 3.3 | 2.8 | 7.9 | 7.6 | 1.1 | 2.7 | 6.9 | 9.7 | 5.25 | 44.42 |
3 | 3.2 | 4.2 | 1.5 | 5.5 | 5.9 | 3.4 | 10.3 | 4.7 | 4.84 | 45.32 |
Average | 5.31 | 44.38 |
Table 14.
Measured values, means, and S/N ratios for surface roughness.
Table 14.
Measured values, means, and S/N ratios for surface roughness.
Experiment Number | Measured Ra Value (μm) | Mean (μm) | S/N Ratio η (dB) |
---|
1 (A1B1C1) | 0.22 | 0.2 | 0.18 | 0.18 | 0.22 | 0.200 | 13.95 |
2 (A1B2C2) | 0.24 | 0.26 | 0.26 | 0.26 | 0.25 | 0.254 | 11.90 |
3 (A1B3C3) | 0.22 | 0.2 | 0.22 | 0.22 | 0.2 | 0.212 | 13.46 |
4 (A2B1C2) | 0.16 | 0.14 | 0.18 | 0.16 | 0.14 | 0.156 | 16.10 |
5 (A2B2C3) | 0.24 | 0.22 | 0.24 | 0.24 | 0.24 | 0.236 | 12.54 |
6 (A2B3C1) | 0.14 | 0.16 | 0.16 | 0.2 | 0.16 | 0.164 | 15.64 |
7 (A3B1C3) | 0.18 | 0.18 | 0.2 | 0.2 | 0.2 | 0.192 | 14.32 |
8 (A3B2C1) | 0.3 | 0.3 | 0.28 | 0.3 | 0.28 | 0.292 | 10.69 |
9 (A3B3C2) | 0.24 | 0.24 | 0.24 | 0.24 | 0.24 | 0.240 | 12.40 |
Table 15.
Response table for S/N ratios for surface roughness.
Table 15.
Response table for S/N ratios for surface roughness.
| Factor | A (Spindle Speed) | B (Feed Rate) | C (Tool Path) |
---|
Level | |
---|
1 | | 13.10 | 14.79 | 13.42 |
2 | | 14.76 | 11.71 | 13.46 |
3 | | 12.47 | 13.83 | 13.44 |
Δmax−min | | 2.29 | 3.08 | 0.04 |
Rank | | 2 | 1 | 3 |
Table 16.
Response table for means for surface roughness.
Table 16.
Response table for means for surface roughness.
| Factor | A (Spindle Speed) | B (Feed Rate) | C (Tool Path) |
---|
Level | |
---|
1 | | 0.2220 | 0.1827 | 0.2187 |
2 | | 0.1853 | 0.2607 | 0.2167 |
3 | | 0.2413 | 0.2053 | 0.2133 |
Δmax−min | | 0.0560 | 0.0780 | 0.0053 |
Rank | | 2 | 1 | 3 |
Table 17.
ANOVA for surface roughness.
Table 17.
ANOVA for surface roughness.
Factor | Degree of Freedom (DF) | Sum of Squares (SS) | Mean Square (MS) | F-Ratio (FX) | Contribution (PX) |
---|
A (spindle speed) | 2 | 8.3888 | 4.1944 | 11.2481 | 30.8% |
B (feed rate) | 2 | 14.9217 | 7.4609 | 20.0078 | 57.2% |
C (tool path) | 2 | 0.0024 | 0.0012 | 0.0032 | -- |
Error | 2 | 1.4892 | 0.7446 | | |
Total | 8 | 24.8021 | | | |
Pooled error | 4 | 1.4916 | 0.3729 | | |
Table 18.
Mean values and S/N ratios for surface roughness from verification experiments.
Table 18.
Mean values and S/N ratios for surface roughness from verification experiments.
Experiment Number | Measured Ra Value (μm) | Mean (μm) | S/N Ratio η (dB) |
---|
1 | 0.14 | 0.16 | 0.18 | 0.18 | 0.12 | 0.156 | 16.04 |
2 | 0.22 | 0.18 | 0.18 | 0.14 | 0.14 | 0.172 | 15.16 |
3 | 0.16 | 0.2 | 0.18 | 0.16 | 0.18 | 0.176 | 15.06 |
Average | 0.168 | 15.42 |