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
Contents Introduction Chatter Modelling Analysis Detection Control Conclusions 2
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
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
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
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
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
The stability limit Quasi-periodic Stability Lobes Diagram Chatter x Depth of cut time Periodic No chatter x Spindle speed time 8
Cutting force Delay τ + + Cutting Machine dynamics + _ sin cos 9
Machine dynamics Delay τ + + Cutting Machine dynamics + _ sin cos 10
Chip thickness Delay τ + + Cutting Machine dynamics + _ sin cos 11
The model Delay τ + + Cutting Machine dynamics + _ sin cos 12
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
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
Stability Secondary Hopf or Period Doubling bifurcation 1 Extra frequency quasi periodic behaviour 0.5 imag(µ) 0 a p -0.5-1 -1-0.5 0 0.5 1 real(µ) Ω 15
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
Simulation of the model Increasing depth of cut X [db] 20 0-20 -40-60 -80-100 Frequency [khz] 30 25 20 15 10 Depth of cut Spindle speed chatter tooth -120-140 5 0 0 500 1000 Time [ms] 17
Frequencies in chatter 10 6 Peaks due to spindle speed components: Peaks due to chatter: Experimental result PSD acceleration 10 4 10 2 10 0 signal f RPM f TPE f chat 10-2 0 2000 4000 6000 8000 10000 Frequency [Hz] 18
Results 10 0 Simulation PSD (y) 10-10 10-20 0 1000 2000 3000 4000 5000 Frequency [Hz] 10-5 Experiment PSD (y) 10-10 10-15 0 1000 2000 3000 4000 5000 Frequency [Hz] 19
Detection Signal contains frequencies 1. Choose frequency band around the -th harmonic FFT signal 10 6 10 4 signal f RPM f TPE f chat 10 2 0 200 400 600 800 1000 Frequency [Hz] 20
Detection 2. Apply bandpass filter around -th harmonic Signal contains frequencies and FFT signal 10 6 10 4 signal f RPM f TPE f chat 10 2 0 200 400 600 800 1000 Frequency [Hz] 21
Detection 3. Apply demodulation: Frequencies shifted with and Signal contains frequencies 0, and FFT signal 10 6 10 4 0 signal f RPM f TPE f chat 10 2 0 200 400 600 800 1000 Frequency [Hz] 22
Demodulation Example: two sinusoids: Demodulation: 23
Experimental set-up Accelerometer Microphone Spindle Toolholder Mounting device Tool Eddy current sensor Workpiece Accelerometer Dynamometer Bed 24
Experimental set-up 1. Microphone 2. Accelerometer 3. Eddy current 4. Dynamometer 5. Accelerometer 6. Mill 7. Workpiece 8. Mounting device 25
Experiments Increasing depth of cut Begin: stable End: chatter Apply detection method to different sensors Force Acceleration Displacement Sound Compare with workpiece surface 26
Sensor choice Detection [m] 5 0-7 x 10 Displacement x 10 x 10-7 Displacement y 10 Detection [m] 5 0 Detection [N] 2 1 0 Force y -5 0 0.5 1 Time [s] -5 0 0.5 1 Time [s] -1 0 0.5 1 Time [s] Detection [m/s 2 ] 2 1 0-1 Acceleration x 0 0.5 1 Time [s] Detection [m/s 2 ] 4 2 0-2 Acceleration y 0 0.5 1 Time [s] Detection [V] 1 0.5 0-0.5 Sound 0 0.5 1 Time [s] 27
Choice of frequency 0.1 1 st harmonic 1 2 nd harmonic Detection 0 0.5 0-0.1 0 0.5 1-0.5 0 0.5 1 4 3 rd harmonic 1 4 th harmonic Detection 2 0 0.5 0-2 0 0.5 1 Time [s] -0.5 0 0.5 1 Time [s] 28
Experimental results 0.6 0.5 0.4 33000 rpm a p 3.0 5.0 mm Full immersion 3 rd harmonic Chatter Detection 0.3 0.2 0.1 Onset 0 Stable -0.1 0 5 10 15 20 Length of cut [cm] 29
Comparison with workpiece 0.4 0.2 0 5 6 7 8 9 10 11 12 13 14 15 16 17 18 30
Chatter control Change spindle speed and feed Depth of cut Spindle speed 31
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
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