Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/91440
標題: A Study on The Effect of Flatness on Assembly Errors of Planar Surface
平面度對平面組裝誤差影響之探討
作者: 張鎮顯
Chen-Hsien Chang
關鍵字: Assembly error of planar surface;tolerance analysis and allocation;flatness;waviness;平面對組裝誤差;公差分析與配置;平面度;波紋
引用: [Requicha, 1983] A. A. Requicha, 'Toward A Theory of Geometric Tolerancing,' International Journal of Robotics Research, Vol.2, No.4, 1983, pp.45-60. [Wang, 1987] H. H. S. Wang, Design Methods for Minimization of Position Error in Linkages. Ph. D. Dissertation, Stanford University, 1987. [Fleming, 1988] A. Fleming, ' Geometric Relationships between Toleranced Features,' Artificial Intelligence, Vol.37, No.1-3, 1988, pp. 403-412. [BjØrke, 1989] O. BjØrke, Computer-Aided Tolerancing, 2nd ed. ASME Press, 1989. [Ward, 1992] K. Ward, Integrating Geometric Form Variations into Tolerance Analysis of 3-D Assemblies, M.S. Thesis, Brigham Young University, 1992. [Tsai, 1993] J.-C. Tsai, Tolerance Reasoning for Concurrent CAD/CAM Systems, Ph. D. Dissertation, Stanford University, 1993. [Whitney & Gilbert, 1993] D.E. Whitney, O. L. Gilbert, 'Representation of Geometric Variations Using Matrix Transformation for Statistical Tolerance Analysis,'Proceedings of IEEE International Conference on Robotics and Automation, Vol.2, 1993, pp.314-321. [ASME Y14.5.1M, 1994] ASME Y14.5.1M, Mathematical Definition of Dimension and Tolerancing Principles, Draft 1994. [Chase et. al., 1995] K. W. Chase, J. Gao, and S. P. Magleby, 'General 2-D Tolerance Analysis of Mechanical Assemblies with Small Kinematic Adjustments', Journal of Design and Manufacturing, Vol.5, No.4, 1995. [Desrochers & Riviere, 1997] A. Desrochers, A. Rivere, 'A Matrix Approach to the Representation of Tolerance Zones and Clearances,' The International journal, advanced manufacturing technology, Vol.13, No.9, 1997, pp.630-636. [Gao et. al., 1998] J. Gao, K. W. Chase, and S. P. Magleby, 'Generalized 3-D Tolerance Analysis of Mechanical Assemblies with Small Kinematic Adjustments,' IIE transactions, Vol.30, No.4, 1998, pp.367-377. [Desrochers et al., 2003] A. Desrochers, W. Ghie, and L. Laperriere, 'Application of A Unified Jacobian-Torsor Model for Tolerance Analysis,' Journal of Computing and Information Science in Engineering, Vol.3, No.1, March, 2003, pp.2-14. [Tang et al., 2011] S.-L. Tang, J.-F. Yu, Y. Li, H.-H. Yang, 'Assembly Tolerance Analysis for Parts with Flatness Based on Virtual Mating Plane,' Computer Integrated Manufacturing Systems, Vol.17, No.4, 2011, pp.711-715. [Grandjean et al., 2013] J. Grandjean, Y. Ledoux, S. Samper, H. Favrelière, 'Form Errors Impact in A Rotating Plane Surface Assembly,' Procedia CIRP 10, 2013, pp. 178–185 [徐衛良&張啟先,1988] 徐衛良、張啟先,'空間機構運動誤差的概率分析和蒙特卡羅模擬',東南大學學報 (自然科學版) ,1988,第18卷第6期。 [鄭國德,1995] 鄭國德,'區間與統計資料運算方法之發展及其在產品誤差分析之應用',國立中興大學機械工程研究所碩士論文,1995。 [侯靖男,1996] 侯靖男,'公差分析與公差敏感度分析在產品設計之應用',國立中興大學機械工程研究所碩士論文,1996。 [郭德寧,1996] 郭德寧,'幾何公差與配合數學模型之建立及其在公差分析之應用',國立中興大學機械工程研究所碩士論文,1996。 [王仁佑,2014] 王仁佑,'閉式靜壓導軌設計與特性分析',國立清華大學動力機械工程研究所碩士論文,2014。
摘要: 
Assembly error can be caused by form tolerances assigned in design. This research is aimed to investigate the effect of form tolerance on the assembly error of a planar pair. Statistical error model is analyzed and constructed to provide the foundation for tolerance analysis and synthesis. This study first established statistical model for planar surface with flatness and waviness. Contact model and resultant error are analyzed using vector analysis based on the planar surface models. The uniqueness of contact model is further investigated with assembled planar surface approaching from various orientations. A statistical error model is developed based on the statistical data. The result shows that the translation error along the normal direction of the planar surface is linearly related to the flatness of the planar surface while errors parallel to the planar surface can be neglected. The orientation error, on the other hand, increases with the flatness and waviness. It is further observed that the average height of contact points decreased while the average height increased. The error model of the assembly of two planar surfaces is established based on the statistical data of these case studies. The developed error model can be used as a basis for tolerance analysis and allocation of precise planar surfaces.

產品在製造時必須訂有合理的公差,為能在設計階段分析產品組裝的誤差,須要分析產品形貌公差對組裝誤差的影響,故本研究探討平面之形貌公差對於組裝誤差的影響,分析並建立平面對組裝之統計誤差模型,提供公差設計與配置之基礎。
本研究首先根據平面度(flatness)以及波紋(waviness)建構平面之統計模型,再以該統計模型及向量分析來分析平面之接觸方式與結果,據以建立具形貌公差之雙平面的組裝誤差,研究亦探討平面組裝時即使不同接觸方向與角度其結果之唯一性,並據此統計不同平面度與波紋對平面對組裝誤差的影響。研究結果顯示,平面對組裝時,平面方向的平移誤差極小,但平面法線方向的平移誤差與角度誤差會隨平面度與波紋增加而提高,此乃因兩參數增加時,會造成平面接觸點高度的平均值下降但平均高度差上升,故影響平面組裝之誤差。本研究最後以平面對組裝之統計數據建立平面對組裝之誤差模型,研究結果可作為精密機械平面對形貌公差設計分析與配置之依據。
URI: http://hdl.handle.net/11455/91440
Rights: 不同意授權瀏覽/列印電子全文服務
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