Abstract
Geometric accuracy of components is one of the most important quality characteristics in layered manufacturing processes on which most rapid prototyping (RP) techniques are based. Layered manufacturing is an approximate fabricating process in which the final geometric error of the physical part is affected, not only by the approximation technique used, but also by the fabrication process. Errors that occur in one layer could propagate and transfer to other layers causing an accumulated error effect in the process. In this paper, a concept of disturbance error is introduced to describe the effect of accumulated errors in the fabrication process. A physical model is presented to describe error interactions and error transfer mechanisms in the layered manufacturing process. A geometrical model is developed using surface approximation techniques to describe the relationships of the geometrical errors. It is shown that although the complexity of the part geometry is not directly related to the manufacturing process, it will affect the geometrical errors of the part produced.
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References
J. P. Kruth, “Material increase manufacturing by rapid prototyping techniques”, Annals CIRP, 40(2), pp. 603–614, 1991.
Xue Yan and P. Gu, “A review of rapid prototyping technologies and systems”, Computer-Aided Design, 28(4), pp. 307–318, 1996.
T. H. C. Childs and N. P. Juster, “Linear and geometric accuracies from layer manufacturing”, Annals CIRP, 43(1), pp. 163–166, 1994.
R. Ippolito, L. Luliano, P. di Torino and A. Gatto, “Benchmarking of rapid prototyping techniques in terms of dimensional accuracy and surface finish”, Annals CIRP 44(1), pp. 157–160, 1995.
P. M. Dickens, “Research developments in rapid prototyping”, Proceedings of the Institution of Mechanical Engineers Part B (Journal of Engineering Manufacture), 209(B4), pp. 261–266, 1995.
Magazine reporter, “Accuracy climbing for rapid prototyping”, Machine Design, 67, pp. 166–167, September 1995.
K. L. Chalasani and A. Bagchi, “Process planning issues in free-form fabrication”, PED-vol 56, Quality Assurance Through Integration of Manufacturing Processes and Systems ASME, pp. 81–92, 1992.
J. L. Ellis, G. Kedem, T. C. Lyerly and D. G. Thielmand, “The racasting engine and ray representations: A technical summary”, International Computational Geometry Application, 1(4), pp. 347–380, 1991.
M. Rajagopalan, HN. M. Aziz and C. O. Huey, “A model for interfacing geometric modeling data with rapid prototyping systems”, Advances in Engineering Software, 23(2), pp. 89–96, 1995.
A. Dolenc, “Rapid recipes for the parametric surface models”, Computers and Graphics, 19(2), pp. 225–236, 1995.
X. Sheng and I. R. Meier, “Generating topological structures for Surface models”, IEEE Computer Graphics and Applications, 15(6), pp. 35–41, 1995.
K. M. Yu and C. L. Li, “Speeding up rapid prototyping by offset”, Proceedings of the Institution of Mechanical Engineers Part B (Journal of Engineering Manufacture), 209, pp. 1–8, 1995.
R. T. Farouki, T. Koenig, K. A. Tarabanis, J. U. Korein and J. S. Batchelder, “Path planning with offset curves for the layered fabrication processes”, Journal of Manufacturing Systems, 14(5), pp. 355–368, 1995.
M. Shahinpoor, “Application of smart materials, structures and systems to free from fabrications”, Proceedings of the Second International Conference on Intelligent Materials, ICIM'94, pp. 1067–1068, 1994.
E. W. Kreutz, G. Backes, A. Gasser and, K. Wissenbach, “Rapid prototyping with CO2 laser radiation”, Applied Surface Science, 86(3), pp. 310–316, 1995.
D. Wimpenny and G. Tromans, “Rapid prototyping and tooling centre”, Manufacturing Engineer, 74(6), pp. 273–275, 1995.
H. Narahara and K. Saito, “Theoretical analysis of laser optics for the rapid prototyping”, Journal of the Japan Society of Precision Engineering, 60(7), pp. 994–998, 1994.
J. Y. H. Fuh, Y. S. Choo, A. Y. C. Nee, L. Lu and K. C. Lee, “Improvement of the UV curing process for the laser lithography technique”, Materials and Design, 16(1), pp. 23–32, 1995.
N. P. Juster, “Rapid prototyping using the selective sintering process”, Assembly Automation, 14(2), pp. 14–17, 1994.
J. L. Beuth and S. H. Narayan, “Residual stress-driven delimitation in deposited multilayers”, International Journal of Solids and Structures, 33(1), pp. 65–78, 1996.
W. Liu, L. Li and A. K. Kochhar, “A method for assessing geometrical errors in layered manufacturing. Part 2: Mathematical modelling and numerical evaluation”, International Journal of Advanced Manufacturing Technology, 14(9), pp. 644–650, 1998.
S. Sartori and G. Zhang, “Geometrical error measurement and compensation of machine”, Annals CIRP, 44(2), pp. 599–609, 1995.
F. Stummel and K. Hainer, Introduction to Numerical Analysis, Scottish Academic Press, Edinburgh, 1980.
Luther Pfahler Eisenhart, An Introduction to Differential Geometry, Princeton University Press, Princeton, 1940.
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Liu, W., Li, L. & Kochhar, A.K. A method for assessing geometrical errors in layered manufacturing. Part 1: Error interaction and transfer mechanisms. Int J Adv Manuf Technol 14, 637–643 (1998). https://doi.org/10.1007/BF01192283
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DOI: https://doi.org/10.1007/BF01192283