Chatter Prediction and Control for High-Speed Milling

Chatter Prediction and Control for High-Speed Milling
Modelling and Experiments
Ronald Faassen
Contents
Nomenclature ix
1 Introduction 1
1.1 High-speed milling . 1
1.2 Chatter . 2
1.3 Modelling the milling process and prediction of chatter . 4
1.3.1 Modelling and analysis . 4
1.3.2 Parameter identification 5
1.4 Chatter detection and control . 6
1.5 Goals and main contribution of the thesis 8
1.6 Outline of the thesis 9
2 Modelling the milling process 11
2.1 The milling process . 12
2.2 Chatter . 16
2.2.1 Stability . 16
2.2.2 Bifurcations . 17
2.2.3 Chatter frequencies . 19
2.3 Tooth path model . 21
2.3.1 Time delay . 24
2.3.2 Chip thickness . 25
2.3.3 Entry and exit angles . 26
2.3.4 Results of the tool path model 27
2.4 Cutting force model 30
2.5 Spindle-toolholder-tool dynamics . 33
2.6 Milling model 33
2.7 Eccentricity . 34
2.8 Time domain simulations . 35
2.9 Discussion 41
3 Stability analysis for chatter prediction 43
3.1 A linearised milling model . 43
3.2 Periodic solution 47
3.3 Results 48
3.3.1 Autonomous model vs. nonautonomous model . 49
3.3.2 Circular tooth path vs. trochoidal tooth path 52
3.3.3 Concentric vs. eccentric tool 56
3.3.4 Feed dependency 59vi Contents
3.4 Discussion 59
4 Experimental identification and validation of the model 63
4.1 Identification of the cutting force parameters 64
4.2 Identification of the spindle-toolholder-tool dynamics 68
4.2.1 Impulse hammer tests . 68
4.2.2 Alternative methods 70
4.3 Validation of the predicted stability lobe . 72
4.4 Discussion 75
5 Online chatter detection 77
5.1 The demodulation method . 77
5.1.1 Demodulation 77
5.1.2 Simulation results . 79
5.1.3 Experimental results 80
5.2 Detection using parametric modelling 86
5.2.1 Box-Jenkins model . 86
5.2.2 Simulation results . 90
5.2.3 Experimental results 92
5.3 Discussion 95
6 Chatter control 97
6.1 Control strategy 97
6.2 Simulation results . 101
6.3 Experimental results 106
6.4 Discussion 110
7 Conclusions and recommendations 111
7.1 Conclusions . 111
7.2 Recommendations . 114
A Floquet theory for DDEs 117
B Finite difference method for DDEs 119
C Stability of DDEs 123
C.1 Method of Altintas and Budak 123
C.2 Semi-discretisation . 126
Bibliography 129
Summary 139
Samenvatting 141Contents vii
Acknowledgements 143
Curriculum vit? 14
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