Abstract
Selection of a building direction is an important step for rapid prototyping regardless of the specific processes used to create the part. It involves the consideration of multi-factors that have influences on surface quality, build efficiency and support structure, etc. Contemporary approaches did not consider the global directional space to search for the optimal building direction. In this paper, we use a multi-sphere model for multi-criteria optimization of building direction in rapid prototyping. Each sphere represents the global directional space for one optimization criterion, and is obtained by uniformly discretizing the surface of a unit sphere. Optimization is then conducted over each discretized spherical surface for each criterion. Two objectives, theoretical volume deviation (TVD) and part height are simultaneously optimized using genetic algorithm. TVD is computed to evaluate the volumetric error along each building direction in a general way. The Pareto front is computed as well in order to study the competing effect from these two criteria. At the end of the paper, examples are presented to show the effectiveness of the method.
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Kamrani AK, Nasr EA (2005) Rapid prototyping theory and practice. Springer, New York
Byun HS, Lee KH (2006) Determination of the optimal build direction for different rapid prototyping processes using multi-criterion decision making. Robotics and Computer-Integrated Manufacturing 22(1):69–80
Ahn D, Kim H, Lee S (2007) Fabrication direction optimization to minimize post-machining in layered manufacturing. Int J Mach Tool Manuf 47(3–4):593–606
Giannatsis J, Dedoussis V (2007) Decision support tool for selecting fabrication parameters in stereolithography. Int J Adv Manuf Technol 33(7–8):706–718
Canellidis V, Giannatsis J, Dedoussis V (2009) Genetic-algorithm-based multi-objective optimization of the build orientation in stereolithography. Int J Adv Manuf Technol 45(7–8):714–730
Nikhil P, Kalyanmoy D (2011) Multi-objective optimization and multi-criteria decision making in SLS using evolutionary approaches. Rapid Prototyping J 17(6):458–478
Rattanawong W, Masood SH, Iovenitti P (2001) A volumetric approach to part-build orientations in rapid prototyping. J Mater Process Technol 119(1–3):348–353
Masood SH, Rattanawong W (2002) A generic part orientation system based on volumetric error in rapid prototyping. Int J Adv Manuf Technol 19(3):209–216
Kumar C, Choudhury AR (2005) Volume deviation in direct slicing. Rapid Prototyping J 11(3):174–184
Zhang J, Li Y (2012) A unit sphere discretization and search approach to optimize building direction with minimized volumetric error for rapid prototyping. Int J of Adv Manuf Technol (accepted). doi:10.1007/s00170-012-4518-0
Hur S-M, Choi K-H, Lee S-H, Chang P-K (2001) Determination of fabricating orientation and packing in SLS process. J Mater Process Technol 112(2–3):236–243
Gogate AS, Pande SS (2008) Intelligent layout planning for rapid prototyping. Int J Prod Res 46(20):5607–5631
Ancau M, Caizar C (2010) The computation of Pareto-optimal set in multicriterial optimization of rapid prototyping processes. Comput Ind Eng 58(4):696–708
Chan CK, Tan ST (2004) Putting objects into a cylindrical/rectangular bounded volume. Computer Aided Design 36(12):1189–1204
Allen S, Dutta D (1995) Determination and evaluation of support structures in layered manufacturing. J of Design and Manuf 5(3):153–162
Thompson DC and Crawford R H (1995) Optimizing part quality with orientation. Proceedings of the 1995 Solid Freeform Fabrication Symposium, Austin, Texas
Kim JY, Lee K, Park JC, Jung YH (1998) Efficient calculation of trapped volumes in the layered manufacturing process. Int J Adv Manuf Technol 14(12):882–888
Cheng W, Fuh JYH, Nee AYC, Wong YS, Loh HT, Miyazawa T (1995) Multi-objective optimization of part-building orientation in stereolithography. Rapid Prototyping J 1(4):12–23
Hur J, Lee K (1998) The development of a CAD environment to determine the preferred build-up direction for layered manufacturing. Int J Adv Manuf Technol 14(4):247–254
Pandey PM, Thrimurthulu K, Venkata NR (2004) Optimal part deposition orientation in FDM by using a multicriteria genetic algorithm. Int J Prod Res 42(19):4069–4089
Saff EB, Kuijlaars ABJ (1997) Distributing many points on a sphere. Math Intell 19(1):5–11
Chen LL, Woo TC (1992) Computational geometry on the sphere with application to automated machining. ASME J of Mechanical Design 114:288–295
Chen LL, Chou SY, Woo TC (1993) Parting directions for mould and die design. Computer-Aided Design 25(12):762–768
Spitz SN, Spyridi AJ, Requicha AAG (1999) Accessibility analysis for planning of dimensional inspection with coordinate measuring machines. IEEE Trans Robot Autom 15(4):714–727
Yang ZY, Chen YH, Sze WS (2001) Determining build orientation for layer-based machining. Int J Adv Manuf Technol 18:313–322
Dhaliwal S, Gupta SK, Huang J, Priyadarshi A (2003) Algorithms for computing global accessibility cones. ASME J of Computing and Inf Sci in Eng 3(3):200–209
Zitzler E, Deb K, Thiele L (2000) Comparison of multi-objective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195
Horn J, Nafpliotis N, Goldberg DE (1994) A niched Pareto genetic algorithm for multiobjective optimization. In: Proceedings of the first IEEE conference on evolutionary computation. IEEE world congress on computational intelligence, 27–29 June, 1994. Orlando, FL, USA:IEEE; 1994
Hajela P, Lin C-y (1992) Genetic search strategies in multicriterion optimal design. Struct Optimization 4(2):99–107
Murata T, Ishibuchi H (1995) MOGA: multi-objective genetic algorithms. In: Proceedings of the 1995 I.E. international conference on evolutionary computation, 29 November–1 December, 1995. Perth, WA, Australia: IEEE; 1995
Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor
Goldberg DE (1989) Genetic algorithms in search. Addison-Wesley, Optimization and Machine Learning
Mitchell M (1996) An introduction to genetic algorithms. MIT Press, Cambridge
Schmitt LM (2001) Theory of genetic algorithms. Theor Comput Sci 259(1–2):1–61
Steuer RE (1986) Multiple criteria optimization: theory, computations, and application. John Wiley & Sons, Inc., New York
Sawaragi Y, Nakayama H, Tanino T (1985) Theory of multiobjective optimization (vol. 176 of Mathematics in Science and Engineering). Academic Press, Orlando. ISBN 0-12-620370-9
Grab CAD (2012) http://grabcad.com/. Accessed 3 July 2012
Li Y, Frank MC (2012) Computing axes of rotation for setup planning using visibility of polyhedral computer-aided design models. ASME J of Manuf Sciand Eng 134, p. 041005(1–10)
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Li, Y., Zhang, J. Multi-criteria GA-based Pareto optimization of building direction for rapid prototyping. Int J Adv Manuf Technol 69, 1819–1831 (2013). https://doi.org/10.1007/s00170-013-5147-y
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DOI: https://doi.org/10.1007/s00170-013-5147-y