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Analysis of minimum zone conicity error utilizing minimum potential energy theory
|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。
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.
|Appears in Collections:||機械工程學系所|
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