Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/2542
標題: 組合公差分析方法之研究
An Investigation on the Analysis Method for Assembled Tolerances
作者: 郭長信
Kuo, Chang-Hsin
關鍵字: Tolerance;公差;mean shift;normal distribution;First four moment;平均值偏移;常態分佈;四階統計慣量
出版社: 機械工程學系所
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摘要: 
現在的產品常由很多零件所組合而成,而且比以前更加複雜及精準;零件和其相鄰零件間可能存在有多重限制的組合關係,以提高產品的特定性能例如剛性或精度。並且在零件大量生產的過程中,每批零件的平均尺寸有偏離設計中間值或是漂移的問題,而整批零件的尺寸分佈形式也可能會因為不同的製程而呈分佈形狀不同的非常態分佈。
在多重限制的組合情形下,最小間隙的配合面是決定最後組合結果的主導者。在本論文中,使用多重限制組合中的最小間隙做為組合性能評估的指標,並以田口損失函數相類似的型式來計算最小間隙指標,以了解一個組合的最小間隙的機率情形。此外,由製程品管的觀點,一個在製程管制下的製程平均值大約會呈一個截尾的常態分佈形式,因此本文提議一截尾常態分佈製程平均值模式,使用此模式,其預估的公差分佈範圍可以被設計得比較寬鬆,因此可以降低各零件的製造成本。緊接著,考慮公差堆積後的分佈並非都是呈標準的常態分佈,因此,本論文中的修正模式計算公差堆疊後的四階統計慣量,並且考慮到歪斜度(skewness)和高崇度(kurtosis)等對於分佈範圍的影響效果。經由加入歪斜度和高崇度對公差分佈範圍的修正,以及將所需的合格機率加以常規化,利用內插法計算非常態分佈下的修正係數,使零件組合後的公差分佈範圍預估結果更正確。
經由比較本論文所發展的最小間隙指標,可以很容易的分析一個具多重限制的組合的干涉或間隙程度;最小間隙指標如果較小,則其組合的精度較佳,因此,可以使用最小間隙指標來評估複雜的組合關係間的鬆緊狀況。對於零件的平均尺寸偏離設計中間值的情形,使用本論文發展的模式,其預估結果與使用蒙地卡羅法模擬一百萬個樣本的模擬結果比較,差異小於0.5%;而對於零件呈非常態分佈的情形,從本論文中的兩個例子的模擬結果顯示,其和蒙地卡羅法的差異分別為0.799%及-1.76%。顯示此提議的模式,在工程的應用上是快而且是足夠準確的。因此,對於有平均值偏離或漂移,或是非對稱的實施例,本提議的模式都是快而且是相對準確的。

Nowadays, the product is more complicated and precision, which can be an assembly combined by a plurality of parts. The parts further can fit to the adjacent parts with multiple constraints for improving the stiffness and accuracy of the assembly. Furthermore, the parts are manufactured by mass production. The average dimension of the parts may shifts or drifts from the nominal value during the manufacturing process. And, the dimension distribution of the parts can be in non-normal distribution since they are manufactured by different manufacture process.
The smallest gap dominates the assembled results for an assembly with multiple constraints. Similar to the Taguchi loss function, the minimum gap index is used to evaluate the performance of the assembly in this thesis. By comparing the minimum gap index, an assembly with less clearance can be easily identified. Besides, from the concepts of quality control for manufacture process, the mean shift or drift is proposed in a form similar to the truncated normal distribution for a controlled process. By this proposed truncated normal mean shift model, the tolerance range of the parts can be designed in a wider tolerance range, that make the components cost down. Furthermore, the distribution of the parts can in the form of non-normal distribution. A modified model is proposed then, which considers the effects of skewness and kurtosis of the resultant distribution. The proposed method, considering the higher order moments and the normalized probability, predicts more accurate resultants by the interpolation method.
With the proposed method, the assembled state of an assembly with multiple constraints can be evaluated. The assembly behaves a higher probability of stiffness, as if the minimum gap index is smaller. For the mean shift studied for the cases represented in this paper, the results show the difference between this model and the Monte Carlo method with 1,000,000 simulation samples is less than 0.5%. The two stack-up examples described in this paper show the predicted errors only 0.799% and -1.76% respectively. The proposed model is fast and comparatively accurate for both the unsymmetrical distribution and process with mean shift.
URI: http://hdl.handle.net/11455/2542
其他識別: U0005-2707201010062300
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