Abstract
Tolerance design is always a challenging task for engineers, since it need to satisfy multidisciplinary functions. Engineering design is done in two stages: assembly design and detail design. In the first stage, an assembly is designed considering certain system level functions and in secondary detail design stage; decomposition of the assembly is done and process tolerancing is employed for the parts. At the secondary detail design stage, designer adopts geometrical dimensioning and tolerancing (GD&T) concepts for process tolerancing. Hence, assembly and detail design are done in different phases with dissimilar perspectives. As a result, geometric tolerance design often lands in conflict, redesign, and in the case of concurrent engineering, costly reiterations are performed. This conflict occurs because of two vital reasons: (1) a gap exists between these two design stages and no common relation between them; (2) GD&T is adopted in the secondary stage, which is not available in primary stage. This paper offers a framework for a design engineer to bridge the gap and to establish the relation between these stages. A nonlinear combinatorial optimization problem is framed based on assembly function requirement (AFR), and tolerance values are optimized with appropriate constraints. Nontraditional Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and differential evolution (DE) algorithms are used to solve the problem. For the allocated position tolerances, appropriate sensitive factors are indicated to facilitate design improvement. Finally, a case study is used to illustrate the complete framework.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
ASME Y14.5M-1994 (1994) Dimensioning and tolerancing. The American Society of Mechanical Engineers, New York
Prabhaharan G, Ramesh R, Asokan P (2007) Concurrent optimization of assembly tolerances for quality with position control using scatter search approach. Int J Prod Res 45(21):4959–4988
Ngoi BKA, Min OJ (1999) Optimum tolerance allocation in assembly. Int J Adv Manuf Technol 15:660–665
Hu J, Xiong G (2005) Dimensional and geometric tolerance design based on constraints. Int J Adv Manuf Technol 26:1099–1108
Mohamed HG (2011) Tolerance optimization problem using a near-to-global optimum. Int J Exp Des Proc Optim 2(4):318–335
Zhang Y, Zongbin L, Jianmin G, Jun H (2011) New reasoning algorithm for assembly tolerance specifications and corresponding tolerance zone types. Comp Aid Des. doi:10.1016/j.cad.2011.06.008
Khodaygan S, Movahhedy MR, Fomani MS (2010) Tolerance analysis of mechanical assemblies based on modal interval and small degrees of freedom (MISDOF) concepts. Int J Adv Manuf Technol 50:1041–1061
Bai G, Zhang C, Wang B (2011) Optimization of machining datum selection and machining tolerance allocation with genetic algorithms. Int J Prod Res doi:10.1080/002075400188924 pages 1407–1424
Pandya G, Amine LE, Cavalier TM (2010) Tolerance design of datum systems. Int J Prod Res. doi:10.1080/0020754011002101901 pages 783–807
Demoly F, Luis T, Eynard B, Dimitris K, Samuel G (2011) Geometric skeleton computation enabling concurrent product engineering and assembly sequence planning. Comp Aid design (article in press) (doi:22.1010/j.cad.2011.09.016)
Zbigniew H, Piotr T (2011) Animated visualization of the maximum material requirement. Comp Aid design (article in press) (doi:28.1011/j.cad.2011.09.028)
Robin C, Bernard A (2011) Functional tolerancing: virtual material condition on complex junctions. Comp Aid design (article in press) (doi:31.1005/j.cad.2011.11.09)
Muthu P, Dhanalakshmi V, Sankaranarayanasamy K (2010) Design and manufacturing tolerances optimization with quality loss functions. Int J Adv Oper Manag 2(1/2):90–107
Andrea R, Michele A, Matteo B, Michele L (2011) Fast genetic algorithm for roundness evaluation by the minimum zone tolerance method. Comp Aid design (article in press) (doi:25.1016/j.cad.2011.03.31)
Yashpal K, Hemant R, Raj BA, Sam A (2008) Minimum-zone form tolerance evaluation using particle swarm optimization. Int J Intell Syst Technol Appl 4(1/2):79–96
Loof J, Soderberg R (2007) Top down decomposition of multi-product requirements onto locator tolerances. Proc. Of ASME IMECE
Iannuzzi M, Sandgren E (1994) Optimal tolerancing: the link between design and manufacturing productivity. ASME Design, Theory and Methodology. DTM 94-Vol. 68, pp.29-42
Mohamed HG (2011) Least sensitive tolerance allocation. Int J Qual Eng Technol 2(4):344–356
Wu Z (1997) Sensitive factor for position tolerance. Res Eng Des 9:228–234
ASME Y14.5.1M-1994. Mathematical definition of dimensioning and tolerancing principles. The American Society of Mechanical Engineers, New York, 1994
Jerome D, Denis T (2008) A tolerancing frame work to support geometric specifications traceability. Int J Adv Manuf Technol 36:894–907
Krulikowski A. Tolerance stack—a self study course, Vol. II, 1992. Effective Training Inc.: Westland, Michigan
Srinivasan V (1999) A geometrical product specification language based on a classification of symmetry groups. Comput Aided Des 31:659–668
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197
Price K, Storn R (1997) Differential evolution: a simple evolution strategy for fast optimization. Dr Dobb’s J 22(4):18–24 and 78
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Saravanan, A., Balamurugan, C., Sivakumar, K. et al. Optimal geometric tolerance design framework for rigid parts with assembly function requirements using evolutionary algorithms. Int J Adv Manuf Technol 73, 1219–1236 (2014). https://doi.org/10.1007/s00170-014-5908-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-014-5908-2