Modelling and detection of machine tool chatter in high speed milling

Transcription

1 Modelling and detection of machine tool chatter in high speed milling Ronald Faassen* Nathan van de Wouw* Ed Doppenberg** Henk Nijmeijer* Han Oosterling** *Dynamics and Control Group **Design & Manufacturing / Department of Mechanical Engineering Industrial Modeling & Control Eindhoven University of Technology TNO Science and Industry November 13th, 2006

2 Contents Introduction Chatter Modelling Analysis Detection Control Conclusions 2

3 Introduction Benefits of high speed versus conventional milling High spindle speeds high productivity Relatively low forces complex workpiece geometry Relative new technique (1990 s) Ω Goal: maximize metal removal rate a e f z a p 3

4 Chatter Heavy vibrations of the cutter Bad surface quality Rapid tool wear Noise Stability Lobes Diagram (SLD) Chatter Chatter No chatter Depth of cut Spindle speed No chatter 4

5 Research goals Chatter control Predict the stability lobes in a fast and reliable way Make a device that ensures a stable cut at high metal removal rate, even if the shape of the lobe changes Gain insight into the qualitative behaviour at the stability limit what is chatter? 5

6 Regenerative chatter V c v c l(ε) l(ε) v(t-τ) v(t-τ) x(t) h stat h stat v(t) 6

7 The model Workpiece f z y Ω φ j v y Tool f z +v x F t F r z x Delay τ + + Cutting Machine dynamics + _ sin cos 7

8 The stability limit Quasi-periodic Stability Lobes Diagram Chatter x Depth of cut time Periodic No chatter x Spindle speed time 8

9 Cutting force Delay τ + + Cutting Machine dynamics + _ sin cos 9

10 Machine dynamics Delay τ + + Cutting Machine dynamics + _ sin cos 10

11 Chip thickness Delay τ + + Cutting Machine dynamics + _ sin cos 11

12 The model Delay τ + + Cutting Machine dynamics + _ sin cos 12

13 Bifurcation Stability Lobes Diagram Quasi-periodic Chatter Depth of cut Spindle speed No chatter Bifurcation diagram Im Re x time Periodic Im x Depth of cut Re time 13

14 The model Set of non-autonomous non-linear delay differential equations Find stability limit using semi-discretisation method* Chatter is born through a bifurcation: stable periodic solution loses stability Bifurcation point: Floquet multipliers cross unit circle * T. Insperger and G. Stépán, Int. J. Num. Meth. Eng., (2004) 14

15 Stability Secondary Hopf or Period Doubling bifurcation 1 Extra frequency quasi periodic behaviour 0.5 imag(µ) 0 a p real(µ) Ω 15

16 Chatter frequencies Stability criterion gives one chatter frequency Interaction chatter frequency and spindle speed with non linear system large number of chatter frequencies One dominant chatter frequency close to the natural frequency of the system 16

17 Simulation of the model Increasing depth of cut X [db] Frequency [khz] Depth of cut Spindle speed chatter tooth Time [ms] 17

18 Frequencies in chatter 10 6 Peaks due to spindle speed components: Peaks due to chatter: Experimental result PSD acceleration signal f RPM f TPE f chat Frequency [Hz] 18

19 Results 10 0 Simulation PSD (y) Frequency [Hz] 10-5 Experiment PSD (y) Frequency [Hz] 19

20 Detection Signal contains frequencies 1. Choose frequency band around the -th harmonic FFT signal signal f RPM f TPE f chat Frequency [Hz] 20

21 Detection 2. Apply bandpass filter around -th harmonic Signal contains frequencies and FFT signal signal f RPM f TPE f chat Frequency [Hz] 21

22 Detection 3. Apply demodulation: Frequencies shifted with and Signal contains frequencies 0, and FFT signal signal f RPM f TPE f chat Frequency [Hz] 22

23 Demodulation Example: two sinusoids: Demodulation: 23

24 Experimental set-up Accelerometer Microphone Spindle Toolholder Mounting device Tool Eddy current sensor Workpiece Accelerometer Dynamometer Bed 24

25 Experimental set-up 1. Microphone 2. Accelerometer 3. Eddy current 4. Dynamometer 5. Accelerometer 6. Mill 7. Workpiece 8. Mounting device 25

26 Experiments Increasing depth of cut Begin: stable End: chatter Apply detection method to different sensors Force Acceleration Displacement Sound Compare with workpiece surface 26

27 Sensor choice Detection [m] x 10 Displacement x 10 x 10-7 Displacement y 10 Detection [m] 5 0 Detection [N] Force y Time [s] Time [s] Time [s] Detection [m/s 2 ] Acceleration x Time [s] Detection [m/s 2 ] Acceleration y Time [s] Detection [V] Sound Time [s] 27

28 Choice of frequency st harmonic 1 2 nd harmonic Detection rd harmonic 1 4 th harmonic Detection Time [s] Time [s] 28

29 Experimental results rpm a p mm Full immersion 3 rd harmonic Chatter Detection Onset 0 Stable Length of cut [cm] 29

30 Comparison with workpiece

31 Chatter control Change spindle speed and feed Depth of cut Spindle speed 31

32 Conclusions (1) Model can be used to predict chatter boundary Model gives insight to chatter from a non-linear dynamics point of view Chatter is born through a bifurcation After the bifurcation a broad frequency range exists One frequency, close to natural frequency, is dominant Simulations coincide well qualitatively with experimental results 32

33 Conclusions (2) Chatter can be detected online by various sensors Accelerometer preferable A priori choice of proper demodulation frequencies Using two sensors, detection can run at four different harmonics in parallel at 20 khz Avoid higher harmonics of tooth passing frequency Early detection of onset of chatter Accurate Cost effective Time for control actions to avoid chatter Change spindle speed 33