Volume 20, Issue 3 (March 2020)                   Modares Mechanical Engineering 2020, 20(3): 751-759 | Back to browse issues page

XML Persian Abstract Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Haji Zahedi S, Moetakef-Imani B. Development of Direct Linearization Method in Tolerance Analysis of Mechanical Assemblies by Using NURBS Curves. Modares Mechanical Engineering 2020; 20 (3) :751-759
URL: http://mme.modares.ac.ir/article-15-31771-en.html
1- Mechanical Engineering Department, Engineering Faculty, Ferdowsi University of Mashhad, Mashhad, Iran
2- Mechanical Engineering Department, Engineering Faculty, Ferdowsi University of Mashhad, Mashhad, Iran , imani@um.ac.ir
Abstract:   (5549 Views)
With the advancement of the manufacturing processes and the continuing need for increasingly precise assemblies, consideration of dimensional and geometric tolerances has been of great importance in tolerance analysis of mechanical assemblies. Therefore, in recent decades, several methods have been developed and implemented for calculating the influences of geometric errors of components on the final performance of the assembly. One of the proposed methods for tolerance analysis is the Direct Linearization Method (DLM). However, DLM has significant advantages in dimensional tolerance analysis, due to simplifications used in this technique, it does not have the ability to solve assemblies including free form profiles. In this research, a new method has been proposed to consider the complex profiles in the process of DLM. In the proposed combination method, rational Bezier curves have been used to define component profiles such as elliptical profiles, cams, edge joints, and non-circular profiles that have a complex error variation. Then, by using principles of DLM and rational Bezier equations, the developed algorithm is successfully accomplished. In this way, we can not only use significant advantages of DLM in dimensional tolerance analysis but also it is possible to solve assemblies including a component with complex profiles without any simplification. The developed hybrid approach has been presented in detail by solving an example of assembly tolerance analysis. Finally, validation has been performed and the accuracy of the proposed approach was confirmed using Monte Carlo simulation.
 
Full-Text [PDF 1006 kb]   (1656 Downloads)    
Article Type: Original Research | Subject: Design and manufacture by computer
Received: 2019/04/7 | Accepted: 2019/07/28 | Published: 2020/03/1

References
1. Morse E, Dantan JY, Anwer N, Söderberg R, Moroni G, Qureshi A, et al. Tolerancing: Managing uncertainty from conceptual design to final product. CIRP Annals. 2018;67(2):695-717. [Link] [DOI:10.1016/j.cirp.2018.05.009]
2. Idrissa D, Beaurepairea P, Homrib L, Gayton N. Tolerance analysis-key characteristics identification by sensitivity method. Procedia CIRP. 2018;75:33-38. [Link] [DOI:10.1016/j.procir.2018.03.308]
3. Gao J, Chase KW, Magleby SP. Generalized 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments. IIE Transactions. 1998;30(4):367-377. [Link] [DOI:10.1080/07408179808966476]
4. Yu J, Zhao Y, Wang H, Lai X. Tolerance Analysis of Mechanical Assemblies Based on the Product of Exponentials Formula. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture. 2018;232(14):2616-2626. [Link] [DOI:10.1177/0954405417703425]
5. Ong JB. Geometric modeling of manufacturing processes variations for model-based tolerance analysis [Dissertation]. Virginia: Virginia Polytechnic Institute and State University; 1994. [Link]
6. Polini W, Bianca M, Colosimo NS, editors. Geometric tolerance analysis. In: Polini W, editor. Geometric tolerances. London: Springer; 2011. pp. 39-68. [Link] [DOI:10.1007/978-1-84996-311-4_2]
7. Marziale M, Polini W. A review of two models for tolerance analysis of an assembly: Jacobian and Torsor. International Journal of Computer Integrated Manufacturing. 2011;24(1):74-86. [Link] [DOI:10.1080/0951192X.2010.531286]
8. Tinoco HA, Durango S. Tolerance analysis of planar mechanisms based on a residual approach: A complementary method to DLM. Mathematical Problems in Engineering. 2019;Article ID:9067624. [Link] [DOI:10.1155/2019/9067624]
9. Chase KW, Jinsong G, Magleby SP, Sorensen CD. Including geometric feature variations in tolerance analysis of mechanical assemblies. IIE Transactions. 2016;28(10):795-807. [Link] [DOI:10.1080/15458830.1996.11770732]
10. Dabling JG, Parkinson R, Adams BL, Chabries DM. Incorporating geometric feature variation with kinematic tolerance analysis of 3D assemblies [Dissertation]. Utah: Brigham Young University; 2001. [Link]
11. Wittwer JW, Chase KW, Howell LL. The direct linearization method applied to position error in kinematic linkages. Mechanism and Machine. 2004;39(7):681-963. [Link] [DOI:10.1016/j.mechmachtheory.2004.01.001]
12. Gholami M, Movahhedy MR. Tolerance analysis of a trigger assembly in direct linearization method. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering. 2009;2(2):1-10. [Persian] [Link]
13. Motakef Imani B, Pour M. Tolerance analysis of flexible kinematic mechanism using DLM method. Mechanism and Machine Theory. 2009; 44(2):445-456. [Link] [DOI:10.1016/j.mechmachtheory.2008.03.010]
14. Pierce SJ, Woodruff GW, Rosen DW. NURBS-based variational modeling as a tool for the analysis of geometric tolerances. Proceedings of DETC97: The 1997 ASME Design Engineering Technical Conference, September 14-17, Sacramento, CA. New York: ASME; 1997. [Link]
15. Goka E, Homri L, Beaurepaire P, Dantan JY. Statistical tolerance analysis of over constrained mechanical assemblies with form defects considering contact types. Journal of computing and information science in engineering. 2019;19(2):021010. [Link] [DOI:10.1115/1.4042018]
16. Homri L, Goka E, Levasseur G, Dantan JY. Tolerance analysis-Form defects modeling and simulation by modal decomposition and optimization. Computer-Aided Design. 2017;91:46-59. [Link] [DOI:10.1016/j.cad.2017.04.007]
17. Schleich B, Anwer N, Mathiru L, Wartzack S. Skin Model Shapes: A new paradigm shift for geometric variations modelling in mechanical engineering. Computer-Aided Design. 2014;50:1-15. [Link] [DOI:10.1016/j.cad.2014.01.001]
18. Schleich B, Wartzack S. Novel approaches for the assembly simulation of rigid skin model shapes in tolerance analysis. Computer-Aided Design. 2018;101:1-11. [Link] [DOI:10.1016/j.cad.2018.04.002]
19. Corradoa A, Polinia W, Moronib G, Petrò S. 3D Tolerance Analysis with manufacturing signature and operating conditions. Procedia CIRP. 2016;43:130-135. [Link] [DOI:10.1016/j.procir.2016.02.097]
20. Teissandier D, Delos V, Arroyave-Tobon S, Ledoux Y. Taking into account form variations in polyhedral approach in tolerancing analysis. Procedia CIRP. 2018;75:202-207. [Link] [DOI:10.1016/j.procir.2018.04.084]
21. Ameta G, Davidson JK, Shah JJ. Statistical Tolerance Analysis with T-Maps for Assemblies. Procedia CIRP2018;75:220-225. [Link] [DOI:10.1016/j.procir.2018.02.021]
22. Ramnath S, Haghighi P, Chitale A, Davidson JK, Shah JJ. Comparative Study of Tolerance Analysis Methods Applied to a Complex Assembly. Procedia CIRP. 2018;75:208-213. [Link] [DOI:10.1016/j.procir.2018.04.073]
23. Chen H, Jin S, Li Zh, Lai X. A comprehensive study of three dimensional tolerance analysis methods. Computer-Aided Design. 2014;53:1-13. [Link] [DOI:10.1016/j.cad.2014.02.014]
24. Cao Y, Liu T, Yang J. A comprehensive review of tolerance analysis models. The International Journal of Advanced Manufacturing Technology. 2018;97:3055-3085. [Link] [DOI:10.1007/s00170-018-1920-2]
25. Imani BM, Hashemian SA. Nurbs-based profile reconstruction using constrained fitting techniques. Journal of Mechanics. 2012;28(3):407-412. [Link] [DOI:10.1017/jmech.2012.71]
26. Lai YL, Chen JH, Hung JP. Development of machinable ellipses by NURBS curves. World Academy of Science, Engineering and Technology, International Journal of Mechanical and Mechatronics Engineering. 2008;2(2):162-169. [Link]
27. Pourazady M, Xu X. Direct manipulations of B-spline and NURBS curves. Advances in Engineering Software. 2000;31(2):107-118. [Link] [DOI:10.1016/S0965-9978(99)00026-5]
28. Zhang HR, Zhan GW, Li W, Wei QY, Li M, Tian YZ. The method of tolerance analysis base on the Monte Carlo. Advanced Materials Research. 2014;1039:140-145. [Link] [DOI:10.4028/www.scientific.net/AMR.1039.140]
29. Gao J, Chase KW, Magleby SP. Comparison of assembly tolerance analysis by the direct linearization and modified Monte Carlo simulation methods. Proceedings of the ASME Design Engineering Technical Conferences, 1995 Sep 17-20, Massachusetts, Boston. New York: ASME; 1995. [Link]
30. Montgomery DC, Runger GC. Applied statistics and probability for engineers. 6th Edition. Washington: Wiley; 2003. [Link]
31. Nigam SW, Turner JU. Review of statistical approaches to tolerance analysis. Computer-Aided Design. 1995;27(1):6-15. [Link] [DOI:10.1016/0010-4485(95)90748-5]
32. Rana R, Singhal R. Chi-square test and its application in hypothesis testing. Journal of Practice of Cardiovascular Sciences. 2015;1(1):69-71. [Link] [DOI:10.4103/2395-5414.157577]

Add your comments about this article : Your username or Email:
CAPTCHA

Send email to the article author


Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.