應用GRG演算法判定真直度與真平度之研究

Application of GRG Algorithm to Judging the Minimum Zone Straightness and Flatness

蕭博文(Po-Wen Hsiao)

指導教授 ： 范書愷

元智大學/工程學院/工業工程與管理學系/碩士(2002年)

摘要

當技術伴隨著時代而演進發展時，產品間的功能日趨強大，而其設計也更為複雜；此時，量測物件是否符合其標準規格，儼然變的更為重要及複雜。例如於量測真直度是一種檢測對物件平面上的存在元素，是否符合為直線的條件判定；而量測真平度是一種檢測對物件平面上的存在元素，是否符合為平面的條件判定。
由於最小平方法（LSE）的計算簡單及唯一解的特性，目前在檢驗產品特性測量上確實被廣泛的使用著。然而此法的最大缺點，乃在於只能夠獲得概似解，它並無法保證所要的結果是否正確無誤，也正因為如此，最小平方法的使用上，有著一定程度的風險存在，因此，它並不是一個很好的判定物件特性的演算法。以此為出發考量，為了減少利用此法所造成的誤判與損失，我們將依ANSI所制訂的最小區域準則，提出由一般化縮減梯度搜尋法（GRG），在判定與解決真直度與真平度兩方面上，可以比最小平方法獲得更為精確之數值結果，因此可作為判定這兩種物件特性之應用。而此處的GRG演算法是藉由使用美國微軟所提供之Office Excel’s Solver物件，即「規劃求解」，來協助我們達成計算之過程。
由於目前的品質檢驗過程大都以電腦或軟體為其檢驗的輔助工具，做為決定是否允收之基準。在講求效率與競爭的時代中，追求高精準與高效率的回饋系統，是目前我們所重視的。本研究另一目的，將利用便捷的網際網路，與具有高流通性質的Excel軟體中之規劃求解物件，建構一可供快速查詢結果之使用者界面，並同時達成及時化之理想。

關鍵字

真直度 ； 真平度 ； 最小平方法 ； 最小區域準則 ； 一般化縮減梯度搜尋法 ； 規劃求解

並列摘要

With the progress of technology, the functions of the products have become stronger, and their designs have also become more complicated. As a result, whether the measurements accord with the specifications appears to be a key issue for the downstream manufacturing steps. For example, the measuring of the straightness is a conditional judgment that verifies if the existing element on the object plane is in accordance with a straight line. Similarly, the measuring of the flatness is a conditional judgment that verifies whether the existing element on the object plane is in accordance with a plane.
On account of the features of its calculational simplicity as well as its solution uniqueness, Least Squares Estimation (LSE) is, thus far, extensively used while measuring the features of the products. The most remarkable shortcoming in applying this method, however, is due primarily to the measuring bias that frequently arises in practice. Consequently, the use of LSE, to some extent, needs to bear a certain level of risk. As such, LSE is not an accurate enough algorithm to judge the features of the object. In order to avoid the misjudgment and loss caused by applying this method, we, in accordance with Minimum Zone Criteria dictated by ANSI Y14.5M, propose using the Generalized Reduced Gradient algorithm (GRG) to obtain a more precise quantitative result than using LSE, in both judging and resolving the straightness and flatness. This method can be taken as the application of judging these two types of features of parts being manufactured. In this research GRG is used to help us measure the minimum zone straightness and flatness by the use of the embedded object of the Office Excel''s Solver.
The current quality inspection process mostly depends upon the computer or software as the auxiliary instrument, which is also considered as the basis of whether the outcome is accepted or not. To retain efficiency and competition, the feedback system in pursuit of high-efficiency and high-preciseness is what we emphasize nowadays. By using both the convenient Internet and the widespread Excel software, this study also aims to construct the user''s interface in which the result can be rapidly inquired, achieving the goal of real time.

並列關鍵字

Straightness ； Flatness ； LSE ； Minimum Zone ； GRG ； Solver

參考文獻

2. ANSI Y14.5M (1994). Dimensioning & Tolerancing, The American Society of Mechanical Engineers, New York.

3. Bazaraa, M.S., Sherali, H.D., and Shetty, C.M. (1993). Nonlinear Programming Theory and Algorithms. 2nd ed., Wiley, New York.

4. Carr, K., and Ferreira, P. (1995). “Verification of Form Tolerances Part I: Basic Issues, Flatness and Straightness,” Precision Engineering, 17, 131-143.

5. Cheraghi, S.H., Lim, H.S., and Motavalli, S. (1996). “Straightness and Flatness Tolerance Evaluation: an Optimization Approach,” Precision Engineering, 18, 30-37.

8. Huang, S. T., Fan, K.C., and Wu, J. H. (1993). “A New Minimum Zone Method for Evaluation Flatness Errors,” Precision Engineering, 15, 25-32.