以有限元素法分析微鑽針的側向及扭轉耦合振動之研究

Abstract

中文摘要

本研究主要係用有限元素法分析微型鑽頭鑽削時之側向及扭轉耦合振動。一般分析之系統其元素節點上具有四個自由度，即垂直主軸方向的兩個側向平移之自由度和側向旋轉自由度，而軸向扭轉之自由度並沒有考慮在內。然而，在實際的高速旋轉鑽削過程中，微型鑽頭系統中的側向及扭轉振動是同時存在的，因此我們不能忽略兩者所產生的耦合效應。 在本文中，我們微型鑽頭係由圓柱、圓錐及預扭轉梁(pre-twisted beam)三部分所組成，預扭轉梁則是模擬微型鑽頭的鑽削部分，且為了更接近實際之情況，將微型鑽頭的三個部分都模擬為Timoshenko梁，並把軸向扭轉之自由度加進微型鑽頭系統，再利用有限元素法建立系統之運動方程式，並考慮偏心力、軸向力和外施扭矩在鑽削時對系統所造成之影響，最後運用Newmark積分法之技巧，並撰寫程式做數值分析。其結果發現當系統只存在偏心力或加入鑽削外力時，側向和軸向扭轉之響應會因耦合關係而相互影響。

Abstract In this research, the finite element formulation is developed to analyze the coupling lateral and torsional vibrations of the micro drill with high speed cutting. However, most of these researches treated the micro drill as a system with four degrees of freedom in each node point and assumed that it is rigid in the torsional direction. There are coupling effects when the lateral and torsional vibrations exist at the same time. In this thesis, our micro drill consist of the cylinder, conical beam and pre-twisted beam. And the flute part of the micro drill is modeled by the pre-twisted beam. For accuracy purpose, the micro drill is modeled by the Timoshenko beam. The dynamic equations of the micro drill system are formulated from the finite element model which consists of the effects of the unbalance force, axial force, and external torque. The five degrees of freedom model are used in performing dynamic analysis of micro drill system. The Newmark Integration method is adopted in this approach. Furthermore, we have written a program to do numerical analysis based on the mathematical model we derived. According to our analysis, the response of lateral and torsional vibrations are affected by each other when the system is under the unbalance force, the axial force, and the cutting torque.