Milling Simulation

Preface ix

Introduction xi

Chapter 1 Cutting Forces in Milling Processes 1

1.1 Formulations of cutting forces 1

1.1.1 Mechanics of orthogonal cutting 1

1.1.2 Cutting force model for a general milling cutter 4

1.2 Milling process geometry 8

1.2.1 Calculations of uncut chip thickness 8

1.2.2 Determination of entry and exit angles 12

1.3 Identification of the cutting force coefficients 24

1.3.1 Calibration method for general end mills 24

1.3.2 Calibration method in the frequency domain 33

1.3.3 Calibration method involving four cutter runout parameters 39

1.3.4 Identification of shear stress, shear angle and friction angle using milling tests 48

1.4 Ternary cutting force model including bottom edge cutting effect 55

1.4.1. Calculations of FB(�) 57

1.4.2. Calculations of FB(�) 57

1.4.3 Calibration of Kqc (q = T, R) 58

1.4.4 Calibrations of Kq,B (q = T, R) 59

1.4.5 Experimental work 61

1.5 Cutting force prediction in peripheral milling of a curved surface 61

1.5.1 Calculations of instantaneous uncut chip thickness 65

1.5.2 Calculations of entry and exit angles 67

Chapter 2 Surface Accuracy in Milling Processes 71

2.1 Predictions of surface form errors 71

2.1.1 Calculation of cutting forces and process geometries 73

2.1.2 Iterative algorithms of surface form errors 81

2.2 Control strategy of surface form error 89

2.2.1 Development of control strategy 89

2.2.2 Verification of control strategy 93

2.3 Surface topography in milling processes 95

2.3.1 Prediction method for flat-end milling 97

2.3.2 Prediction method for multi-axis ball end milling 101

Chapter 3 Dynamics of Milling Processes 115

3.1 Governing equation of the milling process 115

3.2 Method for obtaining the frequency response function 120

3.2.1 Derivation of calculation formulations 121

3.2.2 Identification of model parameters 134

3.3 Prediction of stability lobe 139

3.3.1 Improved semi-discretization method 139

3.3.2 Lowest envelope method 144

3.3.3 Time-domain simulation method 155

Chapter 4 Mathematical Modeling of the Workpiece-Fixture System 165

4.1 Criteria of locating scheme correctness 165

4.1.1 The DOFs constraining principle 165

4.1.2 The locating scheme 168

4.1.3 Judgment criteria of locating scheme correctness 172

4.1.4 Analysis of locating scheme incorrectness 173

4.2 Analysis of locating scheme correctness 175

4.2.1 Localization source errors 175

4.2.2 Fixture modeling 176

4.2.3 Locating scheme correctness 182

4.3 Analysis of workpiece stability 186

4.3.1 Modeling of workpiece stability 186

4.3.2 Solution techniques to the model of workpiece stability 194

4.4 Modeling of the workpiece-fixture geometric default and compliance 201

4.4.1 Source error analysis 201

4.4.2 Workpiece position error 207

4.4.3 Machining error analysis 212

4.5 Optimal design of the fixture clamping sequence 218

4.5.1 Effect of clamping sequence on high-stiffness workpiece 218

4.5.2 Effect of clamping sequence on low-stiffness workpiece 224

4.5.3 Optimization of clamping sequence 225

Bibliography 229

Index 245