廣義傳遞矩陣法於斜柄鑽頭側向及扭轉耦合振動之分析

Abstract

本文主要係用廣義傳遞矩陣法分析鑽頭鑽削時之側向及扭轉耦合振動析，一般傳統傳遞矩陣法，建立之轉軸矩陣是集中質量系統來分析並且只有兩個側向位移自由度及兩個側向旋轉自由度並無軸向扭轉自由度，而本文採用的廣義傳遞矩陣法，將扭轉自由度加入系統中，並且將傳統質量集中之軸改良為連續系統，使得準確度得到提升。 本文分析之鑽頭，主要是由圓柱、圓錐與螺旋槽組成，而螺旋槽頂部為鑽削的部分，為了更加接近真實的情況，將鑽頭的三個部分都模擬為Timoshenko Beam，再利用Hammilton Principle與Harmonic Balance Method之觀念，求得其運動方程式及傳遞矩陣，並考慮偏心力、軸向力以及外施扭矩在鑽削時對系統的影響，最後撰寫程式進行數值模擬分析。

In this thesis, the steady state responses of drill system are analyzed by a modified transfer matrix method. The transfer matrix method is modified in this thesis by representing the transfer matrix of the shaft by continuous systems instead of lumped systems. And the five degrees of freedom model are used in performing dynamic analysis of drill system. Therefore, the accuracy of system is improved. In this thesis, the drill consist of the cylinder, conical beam and flute. For realistic,the drill is modeled by the Timoshenko beam. The dynamic equations of the drill system is derived from Hamilton’s Principle. And the process of derving transfer matrix is relatived to Harmonic Balance Method. The drill system is affected by each other when the system is under the unbalance force, the axial force, and the cutting torque. Final, we have written a program to do numerical analysis about modified transfer matrix.