基於向量式有限元素法之撓性機構準靜態分析研究

A Study of Quasi-Static Analysis for Compliant Mechanisms Based on Vector Form Intrinsic Finite Element Method

王勉力(Mien-Li Wang)

指導教授 ： 李志中

國立臺灣大學/工學院/機械工程學研究所/博士(2022年)

https://doi.org/10.6342/NTU202200812

摘要

為了能有效求解撓性機構與連續體機械臂的大變形問題，本文採用向量式有限元素法(VFIFE)進行分析。VFIFE與數學函數描述結構之方法不同，該方法利用一組質點描述連續體，透過牛頓第二定律建立質點的運動方程式，使用點值描述及途徑單元處理質點位置與時間的關係，透過顯式時間積分法並引入質量阻尼或運動阻尼獲得系統的準靜態解。在向量式有限元素法中採用的顯式中央差分法為條件穩定，為確保系統的收斂性與穩定性，本文進一步深入探討顯式動力學中的穩定性與收斂性問題，採用動力鬆弛法強化系統的收斂效率，以及根據離散轉移函數的理論發展了一質量縮放(Mass scaling)的方式解決穩定性的問題，再利用數個幾何非線性例題驗證本文演算法的準確度、收斂性以及穩定性。在分析撓性機構時，因同時具有剛性與撓性元件，需考量剛柔勁度差異造成數值演算過程的高頻振盪問題及柔體應力集中等問題，本文則利用剛體來描述大勁度的元件建立剛柔耦合的數學模型，應力集中則利用von Mises stress判斷結構是否降伏，以及利用有限元素法軟體(ANSYS與ABQUAS)進行驗證。在繩驅動連續體機械臂模型中，透過力量等效的方式將驅動繩與繩孔間之接觸力等效至中央支柱上，此時連續體機械臂則簡化為一般懸臂梁的問題，最後利用自行開發的三維實驗量測平台驗證本文演算法計算連續體機械臂的準確性。

關鍵字

向量式有限元素法 ； 幾何非線性 ； 剛柔耦合 ； 動力鬆弛法 ； 質量縮放 ； 撓性機構

並列摘要

To solve large deformation problem for compliant mechanisms and continuum robots effectively, a technique named vector form intrinsic finite element (VFIFE) method was employed in this dissertation. The VFIFE describes a continuous body by using a set of particles instead of a mathematical function. The equations of motion for particles can then be established by Newton’s law of motion, and if necessary, a viscous or kinetic damping can be introduced to obtain the steady state of the structure. This dissertation focuses mainly on the development of a stability condition regarding the explicit central difference method used in VFIFE such that the convergence of system’s time integration can be achieved. The process is established and evaluated in combination with a dynamic relaxation method with kinetic damping, and mass scaling derived by transfer function theory. In addition, we extend the algorithm to the motion analysis of compliant mechanisms (CM) and tendon-driven continuum robots. In tendon-driven continuum robots, forces that are generated between the driving tendons and disks are generalized into external forces and applied on the backbone of the continuum robots such that the model is simplified as a cantilever beam problem. As for the CM, a rigid-flexible coupling algorithm is developed to analyze the system that contains rigid and compliant components such that high frequency oscillation caused by high stiffness of the flexible members during the time integration can be avoided. Finally, either experiments or the commercial software are performed to verify the accuracy of algorithm in this work.

並列關鍵字

Vector Form Intrinsic Finite Element Method ； Geometrical Nonlinearity ； Rigid-Flexible Coupling ； Dynamic Relaxation Method ； Mass Scaling ； Compliant Mechanism

參考文獻

參考文獻

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