Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/2563
標題: 最小位能理論在極小區域圓錐度形狀誤差分析之應用
Analysis of minimum zone conicity error utilizing minimum potential energy theory
作者: 黃培興
Huang, Pei-Hsing
關鍵字: conical form error;圓錐度形狀誤差;minimum potential energy;virtual work;profile tolerance;minimum zone solution;極小彈性位能;虛功原理;輪廓誤差;極小區域解
出版社: 機械工程學系
摘要: 
本論文應用最小位能理論之原理研究圓錐體形狀誤差(conical form error)之問題,探討岀圓錐度形狀誤差極小區域解(minimum zone solution)之問題可經由搜尋系統最小彈性位能之方式獲得解決,同時分析系統達到穩定平衡狀態以及獲得最小區域解之必要條件,並提出蒐尋圓錐度形狀誤差極小區域解之演算法。
此極小區域解首先透過最小平方法收斂之結果為初始條件,再經由尋找系統之極小彈性位能之方式,由資料點群中蒐選七組資料點,形成兩同心軸、同錐頂角圓錐表面之模擬系統,所有之量測資料點群將由虛擬彈簧所作用之兩同心軸圓錐機構表面完全包圍在內。其中,當彈簧在系統內收縮作用時,將促使同心軸機構之兩圓錐表面產生逼近之運動,朝向最小彈性位能之方向進行,過程中系統將搜尋符合極小位能原則之接觸點,直到最終整個系統達到穩定狀態為止,此時兩圓錐表面間之法向距離即為元件之圓錐度最小形狀誤差。

This research proposes a novel approach for evaluating the conicity based on the principle of minimum potential energy. The minimum zone conical form error problem is resolved by modeling it with an unreal mechanical system and finding the minimum elastic potential energy of it. The sufficient and necessary condition of the minimum zone criteria is derived, and a computational algorithm is demonstrated.
In this unreal mechanical system, a group of fabricated supports are located at position of each measured data points resided. All supports are enclosed by two fictitious spring-connected conical surfaces with a common axis and vertex angle.
The model of the system in this study is a nonlinear one. At first, the initial solution of the nonlinear system is determined by method of least squares. Secondly, the active seven data points or supports are chosen from the measured data points according to the proposed criterion. The spring in the system will contract and the potential energy of the unreal mechanical system formed by these active data supports will decrease naturally. The system reduces the potential energy by changing the active supports alternatively. Finally, the system will reach a stable state with minimum potential energy. A direct searching technique for finding the minimum zone solution is also recommended. The gap between such two conical surfaces is the minimum zone of conical form error.
URI: http://hdl.handle.net/11455/2563
Appears in Collections:機械工程學系所

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