具直槽或曲槽日內瓦機構之最佳運動性能研究

Abstract

本研究以日內瓦輪角加速度、輸入扭矩、最大接觸應力或磨耗的峰值最小化為最佳化設計的目標函數，提出一個設計直槽日內瓦機構之主動輪角位移函數的方法及一個設計曲槽日內瓦機構之日內瓦輪角位移函數的方法，分別探討以變速度輸入之直槽日內瓦機構的運動性能及以等速度輸入的曲槽日內瓦機構之運動性能。 為了方便稱呼，本研究中稱所提出的兩種方法為直槽變速度輸入法和曲槽等速度輸入法。本研究將主動輪角位移函數視為時間的函數，將日內瓦輪角位移函數視為主動輪角位移的函數。本研究假設擬設計之函數具反對稱性，所以僅設計一半的函數。本研究的方法將擬設計之函數的定義域分成多段，每一段稱為一個元素，每個元素的兩個端點稱為節點，將函數及其微分之節點值當作設計變數，將每個元素內的函數表示成Hermite多項式與函數及其微分之節點值的乘積。為了滿足函數二次微分在節點的連續性，本研究採用二階以上的Hermite多項式。 本研究利用粒子群演算法(particle swarm optimization)求解直槽變速度輸入法的主動輪角位移函數和曲槽等速度輸入法的日內瓦輪角位移函數以及對應的曲槽輪廓。本研究以不同槽數的日內瓦機構、不同的元素數目與不同的目標函數之設計實例說明本研究提出之方法的可行性及有效性，探討日內瓦機構的運動性能，並與文獻上的結果比較。

To investigate the optimal kinematic characteristics of Geneva mechanism with radial straight slots at variable input speed and Geneva mechanism with curved slots at constant input speed, two methods are proposed for optimum design of the crank angular displacement function of the Geneva mechanism with radial straight slots at variable input speed and the wheel angular displacement function of the Geneva mechanism with curved slots at a constant input speed, respectively. In this study, minimizing the peak of four different objective functions for the optimum design are considered, respectively. They are the angular acceleration of the Geneva wheel, the input torque, the contact stress, and the degree of wear. For convenience, the proposed methods are referred to as straight slot-variable input speed method and curved slot-constant input speed method. In this study, the crank angular displacement function is regarded as a function of time and the wheel angular displacement function is regarded as a function of the crank angular displacement. In this study, it is assumed the functions being designed are antisymmetric, thus only half of the functions need to be designed. Here, the domain of the function being designed is divided into several segments. Each segment is called an element, and both ends of each segment are called nodes. The nodal values of the function and its derivatives are used as design variables. The function being designed is assumed to be the Hermite interpolating polynomial in each element. In order to satisfy C2 continuity between elements, nth (n ) level Hermite interpolating polynomial is used. The particle swarm optimization method is employed to solve the optimum problems. Design examples are given to demonstrate the effectiveness and practicability of the proposed method and to investigate the optimal kinematic characteristics of Geneva mechanism.