Abstract
Inaccuracies in conventional tolerance characterization methods, which are based on worst-case and root-square-error methods, as well as inefficiencies in Monte Carlo computational methods of statistical tolerance analysis, require an accurate and efficient method of statistical analysis of geometric tolerances. Here, we describe a unified error distribution model for various types of geometric tolerance to obtain the distribution of the deviations in different directions. The displacement distributions of planes, straight lines, and points are analyzed based on distributions within tolerance zones. The distribution of the displacements of clearance fits is then determined according to the precedence of the assembly constraints. We consider the accumulated assembly variations and displacement distributions, and an analytical model is constructed to calculate the distribution of the deviations of the control points and the process capability index to validate the functional requirements. The efficiency of the method is shown by applying it to the assembly of a single-rod piston cylinder. The results are compared with other statistical methods of tolerance analysis. We find an improvement of approximately 20 % in tolerance analysis, and the process capability index of the assembly procedure was reduced by 10 %.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Nigam SD, Turner JU (1995) Review of statistical approaches to tolerance analysis. CAD Comput Aided Des 27(1):6–15
Jami JJ, Ameta G, Zhengshu S (2007) Navigating the tolerance analysis maze. Comput-Aided Des Appl 4(5):705–718
Hong YS, Chang TC (2002) A comprehensive review of tolerancing research. Int J Prod Res 40(11):2425–2459
Wu Z, ElMaraghy WH, ElMaraghy HA (1988) Evaluation of cost-tolerance algorithms for design tolerance analysis and synthesis. Manuf Rev 1:168–179
Braun PR, Morse EP, Voelcker HB (1997) Research in statistical tolerancing: examples of intrinsic non-normalities and their effects. Proceeding of the 5th C1RP International Seminar on Computer-Aided Tolerancing, Toronto
Shan A, Roth RN, Wilson RJ (1999) A new approach to statistical geometrical tolerance analysis. Int J Adv Manuf Technol 15(3):222–230
Zhihua Z, Morse EP (2003) Applications of the Gapspace model for mulitidimensional mechanical assemblies. ASME J Comput Inf Sci Eng 3(1):22–30
Shen Z, Shah JJ, Davidson JK (2005) Simulation-based tolerance and assemblablity analysis of assemblies with multiple pin/hole floating mating conditions. ASME
Ameta G, Davidson JK, Shah JJ (2007) Using Tolerance-Maps to generate frequency distribution of clearance for tab-slot assemblies. Proceeding of ASME IDETC/CIE, Las Vegas
Ameta G, Davidson JK, Shah JJ (2007) Using tolerance-maps to generate frequency distribution of clearance and allocate tolerances for pin-hole assemblies. J Comput Inf Sci Eng 7(4):347–359
Dantan J-Y, Qureshi A-J (2009) Worst-case and statistical tolerance analysis based on quantified constraint satisfaction problems and Monte Carlo simulation. Comput Aided Des 41(1):1–12
Seo HS, Kwak BM (2002) Efficient statistical tolerance analysis for general distributions using three-point information. Int J Prod Res 40(4):931–944
Lin S-S (1997) Statistical tolerance analysis based on beta distributions. J Manuf Syst 16(2):150–158
Varghese P, Braswell RN, Wang B (1996) Statistical tolerance analysis using FRPDF and numerical convolution. Comput Aided Des 28(9):723–732
Liu SG, Wang P, Li ZG (2008) Non-normal statistical tolerance analysis using analytical convolution method. J Adv Manuf Syst 7(1):127–130
Kuo C-H, Tsai J-C (2011) An analytical computation method for statistical tolerance analysis of assemblies with truncated normal mean shift. Int J Prod Res 49(7):1937–1955
Tsai JC, Kuo CH (2012) A novel statistical tolerance analysis method for assembled parts. Int J Prod Res 50(12):3498–3513
Khodaygan S, Movahhedy MR (2011) Tolerance analysis of assemblies with asymmetric tolerances by unified uncertainty–accumulation model based on fuzzy logic. Int J Adv Manuf Technol 53(5–8):777–788
Whitney DE, Gilbert OL, Jastrzebski M (1994) Representation of geometric variation using matrix transforms for statistical tolerance analysis in assemblies. Res Eng Des 6:191–210
Ghie W, Laperrière L, Desrochers A (2010) Statistical tolerance analysis using the unified Jacobian–Torsor model. Int J Prod Res 48(15):4609–4630
Zhou S, Huang Q, Shi J (2003) State space modeling of dimensional variation propagation in multistage machining process using differential motion vectors. Robot Autom IEEE Trans 19(2):296–309
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chongying, G., Jianhua, L. & Ke, J. Efficient statistical analysis of geometric tolerances using unified error distribution and an analytical variation model. Int J Adv Manuf Technol 84, 347–360 (2016). https://doi.org/10.1007/s00170-015-7577-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-015-7577-1