臺灣博碩士論文加值系統

本文以台灣工業技術研究院機械所開發的串並聯式工具機為例子，進行3-PRS串並聯式機構之動態靈敏度分析之研究。近年來，工具機的發展邁向高精準度化，而結構振動會對加工精度造成負面影響，因此為了提升工具機效能，機構之動態靈敏度分析實有必要深入研究的。
3-PRS串並聯式機構的設計變數包括靜平台尺寸、動平台尺寸、連桿長度、連桿材料密度、連桿半徑、迴轉對接頭剛性和球接頭剛性等。上述參數對工具機動態特性均會有不同的影響。本文首先利用牛頓法推導3-PRS串並聯式機構運動方程式，經由數值積分方法探討各設計變數變化對系統最大振幅的影響。接著再利用逆向運動學理論推導刀具頭軌跡與滑塊進給量之間的關係式，並使用線性化的技巧來處理複雜的三角微分方程式，以求得設計變數及滑塊進给量對系統自然頻率的靈敏度。
根據數值結果顯示，改變動平台半徑，主要影響到模態中與動平台轉角方向自由度較為相關的自然頻率。改變連桿設計變數及迴轉對接頭剛性均影響到模態中與連桿自由度較為相關的自然頻率。而最高的自然頻率只與動平台半徑與球接頭剛性有關。另外，當系統自然頻率的模態中動平台三個轉角方向趨近於零時，這些自然頻率對位置改變的靈敏度很小。

A hybrid machine tool developed by the Industry Technology Research Institute (ITRI) in Taiwan is used to study the dynamic sensitivity of the 3-PRS series-parallel mechanism. In recent years, the development of machine tools trends toward high accuracy. The accuracy of machine tools is affected greatly by structure vibration. In order to improve system characteristics, it is necessary to study the dynamic sensitivity of the mechanism.
The design variables of the mechanism considered in this study include the radii of the base and moving platforms; lengths, densities and radii of the links; the stiffness of revolute and spherical joints. These parameters will greatly affect the dynamic characteristics of the mechanism. The Newtonian approach is employed to formulate the system equations of motion and the Runge-Kutta method is applied to simulate the dynamic responses of tool tip with the design variables. The relation between sliders’ locations and the tool tip profile is derived by the inverse kinematics. A linearization technique is applied to deal with the complex trigonometric differential equations. The dynamic sensitivity can be analyzed by solving the linearized system equations of motion, and the sensitivity of design parameters and different sliders’ location on the natural frequencies are discussed.
Based on the numerical results, it can be found that the natural frequencies associated with the rotational displacements of the moving platform are affected by the radius of the moving platform. The natural frequencies associated with the degree of freedom of links are affected by the parameters of links or the stiffness of revolute joints. The highest natural frequency is only affected by the radius of the moving platform and stiffness of spherical joints. Besides, some system natural frequencies are not sensitive to sliders’ locations when the corresponding mode shapes in the rotational displacements of the moving platform are close to zero.

摘要 I
ABSTRACT III
CONTENTS V
LIST OF TABLES VII
LIST OF FIGURES VIII
NOMENCLATURES XI
CHAPTERS PAGE

CHAPTER 1 INTRODUCTION
1-1 Motivation of Research 1
1-2 Literature Review 2
1-3 Outline 5

CHAPTER 2 KINEMATIC ANALYSIS
2-1 Direct Kinematics 6
2-2 Inverse Kinematics 13

CHAPTER 3 DYNAMIS ANALYSIS
3-1 Formulation of Equations of Motion 20
3-2 Linearization Method 25
3-3 Analysis of System Natural Frequency 26

CHAPTER 4 NUMERICAL RESULTS AND DISCUSSIONS
4-1 The Sensitivity Analysis of System Maximum Response for Design Variables 30
4-2 The Sensitivity Analysis of System Natural Frequencies and Mode Shapes for
Design Variables 31
4-3 The Sensitivity Analysis of System Natural Frequencies for Different Sliders’
Locations 33
4-4 The Sensitivity Analysis of System Natural Frequencies for a Designed Trajectory
34

CHAPTER 5 CONCLUSIONS AND FUTURE STUDY
5-1 Conclusions 59
5-2 Future Study 60

REFERENCE 61

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