本文主旨在研究雙軸孔配合的組件在無約束狀態下變異的情形。研究首先歸納雙軸孔在間隙配合時各種接觸位置的尺度鏈變化，其次將雙軸孔配合分為傳統尺寸標註與包含幾合容差標註兩種方式分別討論。研究的重點在分析當零件尺寸有不同分佈時，組合件關鍵尺度對應的變異情形。研究中發現使用因子模擬法對軸孔配合進行容差分析，能迅速有效估算導出尺度的公稱值與容差。因為沒有適當的解析方式估算正確的導出尺度變異情形，本研究依據蒙地卡羅模擬法的結果做為參考比較的基準。

This work studies the tolerance analysis of the unconstrained assemblies with double bolt-hole fits. The research starts from investigating the variations of dimension chains for the assemblies with double bolt-hole, clearance fit at different contact positions. Then, the components dimensioned by conventional and geometrical methods are discussed separately. This research focuses on the variations of key dimensions of the assembly while the dimensions of the components have different distributions within the allowable limits. It is found that the factor simulation method can effectively estimate the nominal value and tolerance of the resultant dimensions. Since analytical methods are not applicable to the tolerance analysis of assemblies with bolt-hole fits, the data obtained from Monte Carlo simulation is used as the reference for comparison.

[1] E. M. Mansoor, “The Application of Probability to Tolerances Used in Engineering Design”, Proceedings of the ImechE, 178, pp.29-44, 1967.
[2] Z. Wu, W. H. Elmaraghy “Evaluation of cost-tolerance algorithms for design tolerance analysis and synthesis”, Manufacturing Review, Vol.1, No.3, 1988.
[3] D. H., Evans, “An Application of Numerical Integration Techniques to Statistical Tolerancing”, Technometrics, Vol. 9, pp. 441-456, 1967.
[4] O. Bjorke, “Computer-Aided Tolerance ”2nd edition, Division of Production Engineering, 1989.
[5] C. Zang, J. Luo and B. Wang, “Statistical Tolerance Synthesis Using Distribution Function Zones”, International Journal of Production Reasearch, Vol.37, No.17, 1999.
[6] S. D Nigam and J. U Turner., “Review of Statistical to Approaches Tolerance Analysis”, Computer-Aided Design and Applications, Vol.27, No.1, pp.6-15, 1995.
[7] 王冠文, “含雙軸孔配合的容差分析”,台灣科技大學機械工程系, 2009.
[8] J. R. D’Errico and Jr. Zaino, N. A.,, “ Statistical Tolerancing Using a Modification of Taguchi’s Method ”, Technometrics, Vol. 30, No.4, pp.397-405, 1988
[9] H. S. Seo and B. M. Kwak “Efficient Statistical Tolerance Analysis for General Distributions Using Three-Point Information”, International Journal of Production Research, Vol. 40, pp.931-944, 2002.
[10] C. Y. Lin, W. H.n Huang, M. C. Jeng, J. L. Doong, “Study of an Assembly Tolerance Allocation Model Based on Monte Carlo Simulation”, Department of Mechanical Engineering, National Central University, Chung-Ii 320, Taiwun, ROC, Received 18 Deccmher 1995.
[11] J. J. Shah, G. Ameta, Z. Shen and J. K. Davidson, “Navigating the Tolerance Analysis Maze”, Computer-Aided Design and Applications, Vol.4, No.5, pp.705-718, 2007.
[12] 樓景湖 譯, “公差與組合”, 1985.
[13] J. V. Liggett, “Dimensional Variation Management Handbook”, Prentice Hall.
[14] L.L. Lawrence, “Modern Engineering Statistics”, Duxbury Pr, 1997.
[15] C. C. Wu, Z. Chen, G. R. Tang, “Component Tolerance Design for Minimum Quality Loss and Manufacturing Cost”, Computers in Industry, Vol.35, No.3, pp.223-232, 1998.