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Mechanics and Dynamics of the Tool Holder - Spindle Interface

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Mechanics and Dynamics of the Tool Holder - Spindle Interface MECHANICS AND DYNAMICS OF THE TOOL HOLDER - SPINDLE INTERFACE by MEHDINAMAZI B.Sc, Sharif University of Technology A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA April 2006 © Mehdi Namazi, 2006 Abstract This thesis presents a general method for identifying and modeling the tool holder- spindle interface in machine tools, using an experimental technique and the finite element method. The spindle assembly is one of the weakest parts in the machine tool and contributes to the chatter vibrations. The unwanted vibrations lead to a poor surface finish and can damage the tool, tool holder and spindle bearings. The tool holder-spindle interface is the connection closest to the cutting, and its dynamics can affect the stability of the cutting process and the dimensional accuracy of the work-piece. In this thesis, Timoshenko beam elements are used to model the tool holder, and an experimental setup is used to identify the contact stiffness of the interface for CAT and the HSK tapers. The finite-element models of the tool holder and the spindle are coupled through a receptance coupling model. The effect of the drawbar force is investigated as the main factor affecting the dynamics of the interface. It is shown that with an increase in the drawbar force, the dynamic stiffness of the connection between the holder and spindle taper decreases and saturates after a certain force level. The dynamics of various tool holder types is also investigated in the setup as a guideline to select tool holders for low- speed and high-speed milling operations. This thesis also presents the coupling of tool holder dynamics identified through the finite element method with the experimentally identified spindle. The structural dynamics of the spindle with a tool-holder taper is identified experimentally through an inverse receptance coupling technique. The tool holder stick-out and tool are assumed to be a lightly damped linear structure, and its analytically predicted dynamics is coupled to the spindle with the aid of a receptance coupling method. This approach greatly reduces the number of impact modal tests needed to identify the dynamics of the machine at the tool tip after each tool change. The dynamics of the machine tool and the properties of the work-piece material are used to calculate chatter stability lobes. The proposed method is applied on a horizontal machining center and verified experimentally. ii Table of Contents Abstract ii Table of Contents iii List of Tables v List of Figures vii Acknowledgement xi Chapter 1 Introduction 1 Chapter 2 Literature Review 5 2.1 Modeling the Tool Holder-Spindle Interface 5 2.2 Chatter Vibrations 6 2.3 Substructure Coupling and Joint Identification 7 Chapter 3 Modeling and Identification of Tool Holder-Spindle Interface Dynamics.... 12 3.1 Overview 12 3.2 Finite-Element Model of Tapered Connections 12 3.3 Computational Model of Contact Stiffness in Tapered Connections 14 3.4 Contact Stiffness Derivation through Experimental Identification 17 3.5 Finite Element Model of the Experimental Setup 19 3.5.1 Finite Element Model of the Simulated Spindle 19 3.5.2 Finite Element Model of Tool Holder 20 3.6 Contact Stiffness Identification Results 21 3.7 Simulation Results on the Test Setup 26 3.8 Simulation Results on the Machine Tool 27 3.9 Contact Stiffness Derivation Using Contact Elements 32 3.10 Summary 39 Chapter 4 Experimental Analysis of the Dynamics of Tool Holder-Tool Assemblies.... 40 iii 4.1 Overview 40 4.2 Modal Analysis of Tool Holder-Tool Assembly on a Simulated Spindle 41 4.2.1 Modal Analysis on a Short Overhang 42 4.2.2 Modal Analysis on a Long Overhang 44 4.3 Tool Holder Selection and Tool-Tool Holder Joint Stiffness and Damping 46 4.4 The Effect of Drawbar Force Variation on the Dynamics of the Interface 50 4.5 Case Study: Modal Analysis of a Collet Tool Holder on the Machine Tool 56 4.6 Summary 60 Chapter 5 Receptance Coupling of the Spindle and Arbitrary Tool Holder Dynamics 61 5.1 Overview 61 5.2 Receptance Coupling 62 5.3 Inverse Receptance Coupling 64 5.4 Inverse Receptance Coupling - Experimental Procedure 67 5.5 Receptance Coupling of Arbitrary Tool-Tool Holder Assembly to the Spindle 68 5.6 Simulation and Experimental Results 69 5.7 Tool Length Tuning 77 5.7.1 Chatter-Free Machining 78 5.7.2 Optimization for Maximum Productivity 79 5.7.3 Optimization Results 81 5.8 Summary 85 Chapter 6 Conclusions 86 6.1 Conclusions 86 6.2 Future Research Directions 87 Bibliography 88 Appendix A Timoshenko Beam Element Formulations 91 A.l Beam Element Formulations 91 Appendix B Tables of Modal Parameters 95 Appendix C Inverse Receptance Coupling Solution 103 iv List of Tables Table 3.1: Natural Frequencies of a Free-Free CAT 50 Shrink-Fit Holder 20 Table 3.2: Contact Stiffness per Unit Area for CAT 50 Taper Determined by Experimental Identification - 105 mm Overhang Length from the Spindle Face 21 Table 3.3: Contact Stiffness per Unit Area for CAT 40 Taper Determined by Experimental Identification-95 mm Overhang Length from Spindle Face 23 Table 3.4: Contact Stiffness per Unit Area for HSK A63 Taper Determined by Experimental Identification -87 mm Overhang Length from Spindle Face 25 Table 3.5: Comparison of the Contact Stiffness per unit Area for HSK A63 and CAT 40 Taper - 10 kN Drawbar Force 25 Table 3.6: Radial and Rotational Spring Stiffness of CAT 40 Tool Holder - Spindle 29 Table 3.7: Contact Stiffness Constants for CAT 50 Taper Using Contact Elements 36 Table 3.8: Contact Stiffness Constants for CAT 50 Taper for Different Overhang Lengths with 20 kN Drawbar Force 37 Table 4.1: Modal Parameters at 20 kN Drawbar Force for 64 mm Overhang and 16mm Diameter -1st Mode 46 Table 4.2: Static Stiffness and Dynamic Stiffness of the Four Types of Tool Holders - Simulation Results vs. Experimental Results 48 Table 4.3: Percentage Error in Modal Stiffness - Rigid Tool - Tool Holder Connection 49 Table 4.4: Normalized Dynamic Stiffness and Modal Damping of 4 Types of Tool Holders with 64 mm Overhang 50 Table 5.1: Constraints on Tool Overhang and Spindle Speed 83 Table 5.2: Cutting Conditions 83 Table B. 1: Modal Parameters vs. Drawbar Force for Collet Chuck - 10 mm Overhang 95 Table B.2: Modal parameters vs. Drawbar Force for Power Chuck-10 mm Overhang 96 Table B.3: Modal Parameters vs. Drawbar Force for Hydraulic Chuck - 10 mm Overhang 97 Table B.4: Modal Parameters vs. Drawbar Force for Shrink-Fit - 10 mm Overhang 98 Table B.5: Modal Parameters vs. Drawbar Force for Collet Chuck - 64 mm Overhang 99 Table B.6: Modal Parameters vs. Drawbar Force for Milling Chuck - 64 mm Overhang... 100 Table B.7: Modal Parameters vs. Drawbar Force for Hydraulic Chuck - 64 mm OverhanglOl v Table B.8: Modal Parameters vs. Drawbar Force for Shrink-Fit - 64 mm Overhang vi List of Figures Figure 1.1: Spindle Assembly and Tool Holder-Spindle Interfaces 1 Figure 1.2: CAT Spindle Taper (Left) and the HSK Taper (Right) 2 Figure 1.3: Schematic of Angular Mismatch between Spindle Taper and CAT Tool- Holder Tapers 3 Figure 2.1: Chatter Vibration Mechanism in Turning [2] 6 Figure 2.2: Schmitz's Tool Holder - Spindle Assembly Model[32] 8 Figure 2.3: Tool-Tool Holder Joint Model - Rotational and Linear Joint Elements (Model A) versus Two Linear Joint Elements (Model B)[25] 9 Figure 3.1: Schematic of a Tapered Tool Holder inside the Spindle Taper 12 Figure 3.2: Timoshenko Beam Element Model of the Tool Holder-Spindle Interface with Distributed Contact Springs 13 Figure 3.3: Equivalent Rotational Springs 14 Figure 3.4 :Timoshenko Beam Element Model of Tool Holder-Spindle Connection with Distributed Rotational and Radial Springs 15 Figure 3.5: Experimental Setup for Dynamic Analysis of Spindle-Tool Holder Interface.... 18 Figure 3.6: Flowchart for Deriving the Stiffness Constants through Experimental Identification 19 Figure 3.7 : Equivalent Circular Cross-Section of Spindle Block 20 Figure 3.8: Experimental and Finite Element Model of the Free-Free Tool holder 20 Figure 3.9: Frequency Response Function of the CAT 50 Taper in Experimental Setup - 20 kN Drawbar Force 22 Figure 3.10: Frequency Response Function of the CAT 40 Taper in Experimental Setup - 10 kN Drawbar Force 23 Figure 3.11: HSK A63 Shrink-Fit Tool Holder 24 Figure 3.12 : Spindle Block - HSK A63 Tool Holder Assembly 24 Figure 3.13: Frequency Response Function of the CAT 50 Shrink-Fit Holder with a 64 mm Overhang Blank Tool in Experimental Setup - 20 kN Drawbar Force 26 Figure 3.14 : Frequency Response Function of the CAT 50 Shrink-Fit Holder with a 15 mm Overhang Blank Tool in Experimental Setup - 20 kN Drawbar Force 27 vn Figure 3.15 : Finite Element Model of Spindle System on Machine 28 Figure 3.16 : Finite Element Model of Tool Holder in Spindle Taper with Connection Springs 28 Figure 3.17: Frequency Response Function at the Tool Tip 30 Figure 3.18 : Mode Shapes Contributed by Tool - Tool Holder Assembly 31 Figure 3.19 : Schematic of Bending Deformations of the Tool Holder - Spindle Interface.. 32 Figure 3.20: 3D Finite Element Model of Tool Holder in Spindle Taper with Boundary Conditions - Model A 34 Figure 3.21: 3D Finite Element Model of Tool Holder with Rigid Spindle-Tool Holder Connection - Model C 34 Figure 3.22: The Effect of Drawbar Force on the Static Stiffness of a CAT 50 Tapered Connection - Simulation Results 35 Figure 3.23: Finite Element Model of Tool Holder in Spindle Taper using Timoshenko Beam Elements 36 Figure 3.24 : Flowchart for Obtaining the Stiffness Constants by Using Contact Elements.
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