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Chapter 1 Introduction 1.1 Machine tool vibration 1.2 Influence of feed system vibration 1.3 The current status of feed system vibration 1.3.1 The establishment method of analytical model 1.3.2 The method of vibration control References Chapter 2 The Vibration Modal Analysis of the Ball Screw about Machine Tools 2.1 Introduction 2.2 Physical model of feed system 2.3 Mechanical model of ball screw 2.4 Analysis of speed ball screw based on FEM 2.5 Modal experiment of ball screw 2.5.1 Modal experiment scheme 2.5.2 Analysis of experimental results References Chapter 3 Rigid-flexible Coupling Model and Dynamic Characteristic Analysis of Feed System 3.1 Introduction 3.2 Mathematical modeling 3.2.1 Dynamic model of linear guide pair 3.2.2 Dynamic model of ball screw 3.3 Establishment of rigid-flexible coupling model 3.3.1 Establishment of the flexible body model 3.3.2 Rigid body model establishment and simulation parameter setting 3.4 Analysis of simulation results 3.4.1 Correlation analysis 3.4.2 The influence of damping coefficient and stiffness on vibration References Chapter 4 Static Stiffness Analysis of Feed System 4. 1 Introduction 4.2 Mathematical model of axial static stiffness 4.2.1 A universal model of axial static stiffness of ball screw pair 4.2.2 Axial static stiffness of nut 4.2.3 Axial static stiffness of angular contact ball bearings 4.2.4 Axial static stiffness caused by torsional deformation of the screw 4.3 Validation of axial static stiffness model 4.4 Influence of various factors on axial static stiffness 4.4.1 Axial load 4.4.2 Number of balls 4.4.3 Contact angle 4.4.4 Helix angle of the lead screw 4.4.5 Displacement of the workbench 4.4.6 Rigidity of each component References Chapter 5 Influence of Dynamic Stiffness on Vibration of Feed System 5.1 Introduction 5.2 Dynamic model considering coupling stiffness 5.3 Experimental verification of dynamic rr[odel 5.4 Vibration characteristic analysis References Chapter 6 Influence of Damping Property on Chatter of Feed System 6.1 Introduction 6.2 Dynamic model based on the Lagrange equation 6.3 Simulation analysis 6.3.1 Simulation parameter setting 6.3.2 Simulation result analysis References Chapter 7 Axial Non-linear Vibration of Feed System 7. 1 Introduction 7.2 Theoretical modeling 7.3 Numerical simulation 7.3.1 Ball-screw length L 7.3.2 Exciting force F 7.3.3 Excitation frequency �� 7.3.4 Damping ratio c 7.4 Experimental verification References Chapter 8 Adaptive Control of Feed System Based on LuGre Model 8.1 Introduction 8.2 Dynamic modeling of the feed system 8.3 Designing of the friction compensation controller 8.4 Simulating of adaptive friction compensation References