Analysis of milling stability based on cutting force signal processing

國國國國國國國國 國國國國國 國國國國 國國 國國國 M 10 國國國國國國國國國國國國國國國 Analysis of Milling Stability Based on Cutting Force Signal Processing (Draft) 國國國國Tran Minh Quang 國國國國國Chun-Hui Chung, Meng -Kun Liu 國國國國 國國國 國 國國 國國國 國國 國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國 國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國 國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國 國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國 國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國 國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國 國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國 國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國 國國國國國國國國-國國國國國國國國國國國國國國國國國國國國國國國國國 國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國 國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國 國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國 國國國國國國國國國國國國國 standard deviation 國國國國國國國國國國國國 國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國國 國國國國國國國國國國國國國國國國 國國國國國國國國國國國國國國國國國國國國國國國國國國國國-國國國 i Abstract The milling operation is the most common form of machining Because the action of each cutting edge and workpiece is intermittent and periodical, the chip thickness varies periodically This could lead to self-excited vibrations and unstable cutting which is called chatter vibration Chatter causes machining instability and reduces productivity in the metal cutting process It has negative effects on the surface finish, dimensional accuracy, tool life and machine life Chatter identification is therefore necessary to control, prevent, or eliminate chatter and to identify the stable machining condition A dynamic cutting force model of the end-milling process with tool runout error was established in this research to understand the underlying mechanism of chatter The accuracy of the cutting force model in both time and frequency domains was evaluated by comparing to experimental force signals Time- frequency analysis approaches, specifically short time Fourier transform, continuous wavelet transform and Hilbert-Huang transform, were utilized to give an utterly different perspective of chatter from the conventional Fourier spectrum which is insufficient in analyzing the signals of rich nonlinear characteristics By comparing the simulation with experimental result, chatter frequency was found to consist of two major components, frequency modulation alongside tooth passing frequency caused by the increased tool runout error and the non-stationary high frequency from the regenerative vibration Moreover, dimensionless chatter indicators, defined by the standard deviation and energy ratio of the specific intrinsic mode function, could identify the occurrence of chatter effectively The analysis result was then validated by the workpiece surface topography, surface roughness and the stability lobe diagram Keywords: Milling process, Chatter detection, Time-frequency analysis, Wavelet transform, Hilbert Huang transform ii Acknowledgement I would like to thank all the people who helped me to finish this thesis First of all, I would like to express my deep gratitude to my academic advisors: Professor Chun-Hui Chung and Professor Meng-Kun Liu for their valuable guidance, encouragement, and support throughout my work towards this thesis Without their help and guidance, this work would not be possible I also would like to thank Mr Yi-Wen Qui who provided his experimental data which was used to verify my methodology in this thesis I would like to thank all of my labmates who have supported me a lot with laboratory facilities so that I could conduct my experiments I thank my friends who always give me encouragements and supports during my research Finally, I would like to thank my parents who always give me love, encouragement, and support throughout my life I would specially thank my wife and my son for their patience and support during my study I am very grateful for their love iii Nomenclature radial and tangential edge db discretized axial depth of cut (mm) Kne , Kte dF differential radial cutting force (N) Nt number of flutes r edge radius (mm) n dFt differential tangential cutting force (N) differential cutting force in x-direction dF (N) x differential cutting force in y direction dFy (N) x, y z coefficients (N/mm) displacement in x and y directions (mm) absolute value of the distance from the end (mm) ft feed per tooth (mm/flute)  helix angle (deg) Fs sampling rate frequency (Hz)  immersion angle (deg) Fsi simulated cutting force (N) e exit angle (deg) Fex experimental cutting force (N) s start angle (deg) b axial depth of cut (mm) c chatter frequency (rad/s) h instantaneous chip thickness (mm)  spindle speed (rpm) Ks specific cutting force coefficient (N)  position angle (deg)  cutting force angle (deg)  runout of cutting edge (mm)  time for one rotation (sec) K n , Kt radial and tangential cutting coefficients (N/mm2) iv Contents 國 國 i Abstract ii Acknowledgement iii Nomenclature iv Contents v Chapter Introduction 1.1 Background 1.2 Objective and Scope 1.3 Outlines and Contribution of the Chapters Chapter Literature Review 2.1 Chatter Vibrations in Milling 2.2 Signal Analysis Approaches Chapter 10 Dynamic Cutting Force Model 10 3.1 Regenerative Chatter Model 10 3.2 Dynamic Cutting Force Model 15 Chapter 17 Experimental Setup and Model Verification 17 4.1 Overview and Aim 17 4.2 Experimental Setup 17 4.2.1 Machine, Cutter and Workpiece 17 4.2.2 Cutting Force Measurement Equipment 19 4.2.3 Surface Topography Measurement Equipment 20 4.2.4 Surface Roughness Measurement Equipment 20 4.3 Cutting Force Coefficients 21 4 Experimental Design Parameters 25 4.5 Tool Tip Dynamics 27 4.5.1 Impact Testing 27 4.5.2 Modal Analysis 27 4.5.3 Stability Lobe Diagram 31 4.6 Simulation and Experimental Results 33 Chapter 36 Chatter Detection Methodology 36 5.1 Short-Time Fourier Transform Analysis 36 5.2 Continuous Wavelet Transform Analysis 38 5.3 Time-Frequency Analysis Based on HHT 41 5.3.1 Chatter Detection Methodology 41 5.3.2 Results and Discussions 44 5.3.3 Dimensionless Indexes for Chatter Identification 50 5.3.4 Method Verification 51 5.4 Chatter Identification in Small Size of End Mill 54 5.4.1 Overview and Aim 54 5.4.2 Experimental Setup 54 5.4.3 Chatter Identification by Time-Frequency Analysis 57 Chapter 60 Conclusions and Future Works 60 6.1 Conclusions 60 6.2 Future Works 60 Bibliography 61 vii 5.3.3 Dimensionless Indexes for Chatter Identification Although chatter could be observed from the analysis tools such as Fourier transform, continuous wavelet transform, and instantaneous frequency, it is still necessary to identify chatter quantitatively for practical applications The standard deviation and energy ratio of the specific IMF are suggested as dimensionless chatter indicators that can be calculated by using Eqs (5-9) and (5-10) respectively In the unstable cutting condition, chatter causes a rapid increase in standard deviation and energy ratio values in IMF2 These values could therefore be used as the dimensionless indicators to identify chatter The presence of chatter could be clearly indicated in Table 5-2 and Table 5-3 when the spindle speeds are at 3000, 3750, 4500, and 5250rpm with the DOC of 1.4 and 1.6mm Unstable cutting conditions were also found at spindle speed of 5250rpm with the DOC of 1.0 and 1.2mm The thresholds of standard deviation and energy ratio of IMF2 were and 0.05, respectively The cutting would be unstable if the indicator value is larger than the threshold On the other hand, the stable cutting is still maintained Table 5-2 The energy ratio values of IMF2s Depth of cut (mm)  (rpm) 0.4 0.6 0.8 1200 9.9 x10-5 8.5 x10-5 7.2 x10-5 3.4 x10-5 6.9 x10-5 7.2 x10-5 2.8 x10-5 1500 2.8x10-4 8.2x10-5 3.6x10-4 1.5x10-4 3.2x10-4 2.1x10-4 2.8x10-4 2250 2.3x10-4 9.1x10-4 3.2x10-4 1.1x10-4 1.3x10-4 1.2x10-4 7.0x10-4 3000 3.6x10-4 7.8x10-4 5.8x10-4 7.3x10-4 1.8x10-4 0.051 0.13 3750 5.2x10-4 1.8x10-4 3.7x10-4 8.6x10-5 4.2x10-4 0.054 0.19 4500 3.9x10-4 6.1x10-4 1.4x10-3 9.5x10-4 5.5x10-4 0.2 0.3 5250 3.15x10-5 3.78x10-5 2.82x10-5 0.17 0.09 0.13 0.21 Bold: unstable cutting 1.0 1.2 1.4 1.6 Table 5-3 The standard deviation values of IMF2s  (rpm) Depth of cut (mm) 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1200 0.14 0.19 0.23 0.19 0.33 0.36 0.31 1500 0.2 0.15 0.41 0.35 0.45 0.51 0.8 2250 0.17 0.42 0.32 0.2 0.3 0.28 0.91 3000 0.16 0.31 0.34 0.46 0.27 4.52 5.15 3750 0.2 0.14 0.23 0.43 0.36 6.5 7.23 4500 0.15 0.23 0.4 0.41 0.37 11.22 12.7 5250 0.12 0.10 0.11 4.28 3.07 4.15 6.35 Bold: unstable cutting 5.3.4 Method Verification The decisions made by chatter indicators showed good agreement with the stability lobe diagram in most experiments except the cases at the stability margin, as indicated in Fig 5.14 The difference was possibly because of the linearization procedure conducted when deriving the stability lobe diagram which would inevitably misinterpret the stability of the cutting process The proposed indicators hence provided a reliable alternative to determine chatter The surface topography images of the machined surface in Fig 5.15 were utilized to validate the result from the indicators as well The irregular wavy surfaces are manifested in Fig 5.15 (d), (e) and (f), which represent the occurrence of chatter On the contrary, the surface topography images in Fig 5.15 (a), (b) and (c) illustrate very consistent cutting marks which indicate the stable cutting conditions All these results are in good accord with that obtained from the signal processing Evidently, the proposed approach could detect chatter accurately and effectively Figure 5.14 Stability lobe diagram and the stability determined by proposed method Figure 5.15 Microscopic of the surface machined with different spindle speed and constant depth of cut of 1.4 m Table 5-4 Surface roughness measured along the feed direction at different cutting conditions DOC (mm) Spindle speed (rpm) Average surface roughness (μm) 1.4 1200 1500 2250 3000 3750 4500 1.698 1.216 0.307 0.591 0.649 0.638 The surface roughness under different milling conditions was measured along the feed direction and provided in Table 5-4 to show the evidence of chatter along with surface topography images It can be seen that the surface roughness (Ra) decreases with the increase of the spindle speed from 1200 to 2250 rpm under stable cutting conditions On the other hand, at the spindle speed of 3000, 3700 and 4500 rpm, the surface roughness does not decrease continuously but suddenly increase The increase of surface roughness values in those cases is resulted by the irregular wavy surfaces manifested in Fig 5.15 (d, e, f) in which the clear evidence of chatter was showed 5.4 Chatter Identification in Small Size of End Mill 5.4.1 Overview and Aim In this section, the method for chatter detection proposed in the previous section is applied to detect chatter in slender end mill Because of small tool diameter, the stiffness of tool is reduced This makes the cutter weak and causes deflection and instability easily during cutting process When the diameter of cutter is down to or mm, it is become difficult to conduct impact testing which is demanded to create the stability lobe diagram A method for chatter detection based on cutting force signal plays an important role in determining the rage of stable cutting conditions This chapter introduces the machines and equipment used to conduct the experiments when mm diameter of end mill was utilized The cutting force signals obtained from different cutting conditions are processing by using proposed method 5.4.2 Experimental Setup Machining experiments were performed in a five-axis CNC milling machine shown in Fig 5.16 The machine features are provided in Table 5-5 The workpiece was a block of Al6061-T6 with size of 30x40x30mm Figure 5.17 represents an uncoated carbide end mill cutter used in following experiments Its diameter is mm, with helix angle of 30° and two flutes The cutting tool parameters in detail are shown in Table 5-6 As the same to previous part, the cutting force signals were also measured directly by using a Kistler dynamometer (type 9129AA) The dynamometer was mounted between the workpiece and workbench Figures 5.18 shows the whole experimental setup Figure 5.16 Five-axis CNC milling machine Table 5-5 Machine’s features Mini 5–Axis-CNC Machine size 75x70x172 cm Max Speed 24000 RPM Max Power 750 W Table diameter φ130 mm Axis travel X 200 mm Y 150 mm Z 180 mm B (+)110 ~ (-)30° C 360° Figure 5.17 A carbide end mill Table 5-6 Parameters of Tool Tool company Tool diameter Flutes (mm) YCHI Cutting edge length (mm) Figure 5.18 Experimental setup In order to examine the dynamic cutting force model and to investigate the proposed methodology for chatter identification, a series of end milling experiments were conducted The cutting force signals in the feed direction were measured from the cutting experiments conducted with different sets of cutting parameters shown in Table 5-7, in which the feed rate was a constant value of 250 mm/min The DOCs ranged from 0.1 to 0.8 mm, while the spindle speeds ranged from 15000 to 22500 rpm The topographical images of the machined surface from cutting experiments were obtained by using the optical microscope (Olympus BX51) with CCD sensor Table 5-7 Experimental design parameters Spindle peed Feed rate of 250 mm/min Depth of cut (mm) 0.1 0.3 0.5 0.8 15000 A1 A2 A3 A4 18000 B1 B2 B3 B4 22500 C1 C2 C3 C4 5.4.3 Chatter Identification by Time-Frequency Analysis The cutting forces in x direction which were obtained from experiments are extracted into a set of IMFs by using EEMD The Hilbert Transform was then applied on each IMF to determine the instantaneous frequency that represents both of time and frequency domain The standard deviation and energy ratio values that proposed in the previous section are utilized to identify the chatter during the milling processes Table 5-8 and 5-9 show all the values of standard deviation and energy ratio corresponding to the cutting condition shown in Table 5-7 It can be seen that all of the standard deviation and energy ratio values are larger than the thresholds that proposed in the previous section except the cutting condition at a spindle speed of 15000 rpm, 0.1 mm depth of cut Therefore, those cutting conditions lead to chatter during machining Table 5-8 The standard deviation values of IMF2s (mm)Depth of cut Feed rate of 250 mm/min Spindle speed (rpm) 0.1 0.3 0.5 0.8 15000 0.486 1.066 2.0241 1.3872 18000 1.1817 1.4034 1.9941 1.5650 22500 1.9699 2.6514 2.6074 3.9132 Table 5-9 The energy ratio values of IMF2s Depth of cut (mm) Feed rate of 250 mm/min Spindle speed (rpm) 0.1 0.3 0.5 0.8 15000 0.2399 0.1823 0.0726 0.0545 18000 0.4624 0.2130 0.1199 0.0490 22500 0.3850 0.2905 0.1259 0.1315 The surface topography images of the machined surface in Fig 5.19 were utilized to validate the result from the indicators in Table 5-8 and 5-9 as well The irregular wavy surfaces are manifested in all experiments except the cutting condition (A1) reveal the occurrence of chatter at those cutting conditions With the condition of spindle speed of 15000 rpm and 0.1 mm depth of cut, on the other hand, the marks left by cutter present quite consistent which indicate the stable cutting conditions All these results are in good accord with the signal processing results Evidently, even though in the small size of end mill, the proposed approach could identify chatter accurately and effectively Spindle speed (rpm) 15000 18000 0.1 0.3 0.5 0.8 Figure 5.19 Machined surface topography 59 22500 Chapter Conclusions and Future Works 6.1 Conclusions Chatter detection plays an important role in improving productivity by providing a range of stable cutting conditions A dynamic cutting force model of the end-milling process has been presented in this paper to understand the underlying mechanism of chatter The stability of the milling process was investigated based on time-frequency analysis approaches, and STFT, WT and HHT were utilized in this study The results indicated that both of WT and HHT approaches are more suitable to identify chatter Chatter was then interpreted from a distinct perspective which defines chatter frequency as the combination of two major components, frequency modulation alongside tooth passing frequency caused by the increased tool runout error and the non-stationary high frequency from the regenerative vibration In addition, the standard deviation and energy ratio of the specific IMF of cutting force signals were proposed as chatter indicators which increase observably as chatter occurs, while their values were close to zero in stable cutting conditions The proposed method was validated by comparing its results to the stability lobe diagram and the machined surface topography along with surface roughness As a result, the approach presented in this study showed the potential to identify chatter effectively 6.2 Future Works For future works, the elastic deformation of the workpiece and cutter in the cutting zone can consider developing the cutting force model The tool wear effected by machining instability will be investigated as well Time-frequency analysis can be utilized for 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