Abstract
Fused Deposition Modeling (FDM) is one of the most used 3D technology for rapid prototyping of different parts. The approach consists in determination of the statistical significance of different parameters using the Analysis of Variance (ANOVA) technique followed by the determination of the correlation laws between the input and output data. These laws are usually described by polynomials obtained with the aid of the Least Squares Method. The use of this method is preferred due to its simplicity, but it has the disadvantage that the error is not known (the only thing we know is that the obtained polynomial leads to the smallest error in the sense of the Least Squares). In our paper we purpose a new approach by using the Tchebyshev polynomials which lead to the mini-max approximation of the law. In this way, the error is always zero in the division points and, moreover, the great advantage is that the error is the smallest one for the entire interval of the input data. The theoretical difficulty of this approach consists in the determination of the division points, while the practical disadvantage is the use of irrational division points for the input data. The formula obtained for the law of variation of the output with respect to the input is the most accurate one in the class of certain polynomials.
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References
Casavola, C., Cazzato, A., Moramarco, V., Pappalettere, C.: Orthotropic mechanical properties of fused deposition modelling parts described by classical laminate theory. Mater. Des. 90, 453–458 (2016)
Casavola, C., Cazzato, A., Moramarco, V., Pappalettera, G.: Residual stress measurement in fused deposition modelling parts. Polym. Test. 58, 249–255 (2017)
Chacón, J.M., Caminero, M.A., García-Plaza, E., Núńez, P.J.: Additive manufacturing of PLA structures using fused deposition modelling: effect of process parameters on mechanical properties and their optimal selection. Mater. Des. 124, 143–157 (2017)
Faes, M., Ferraris, E., Moens, D.: Influence of inter-layer cooling time on the quasi-static properties of ABS components produced via fused deposition modelling. Procedia CIRP 42, 748–753 (2016)
Langelaar, M.: Topology optimization of 3D self-supporting structures for additive manufacturing. Addit. Manuf. 12, 60–70 (2016)
Lee, J., Prabhu, V.: Simulation modeling for optimal control of additive manufacturing processes. Addit. Manuf. 12, 197–203 (2016)
Lindgren, L.E., Lundbäck, A., Fisk, M., Pederson, R., Andersson, J.: Simulation of additive manufacturing using coupled constitutive and microstructure models. Addit. Manuf. 12, 144–158 (2016)
Mohamed, O.A., Masood, S.H., Bhownik, J.L.: Characterization and dynamic mechanical analysis of PC-ABS material processed by fused deposition modelling: an investigation through I-optimal response surface methodology. Measurement 107, 128–141 (2017)
Ravi, P., Shiakolas, P.S., Welch, T.R.: Poly-l-lactic acid: pellets to fiber to fused filament fabricated scaffolds, and scaffold weight loss study. Addit. Manuf. 16, 167–176 (2017)
Sood, A.K., Ohdar, R.K., Mahapatra, S.S.: Experimental investigation and empirical modelling of FDM process for compressive strength improvement. J. Adv. Res. 3, 81–90 (2012)
Stănescu, N.D., Beșliu-Gherghescu, M.L., Tabacu, Ș., Popa, D., Rizea, A., Iordache, M.: The determination of the dependency between the input and output parameters in fused deposition modeling (FDM) using multi polytropic functions. In: Proceedings of the 4th International Congress of Automotive and Transport Engineering (AMMA 2018) (in press)
Teodorescu, P., Stănescu, N.-D., Pandrea, N.: Numerical Analysis with Applications in Mechanics and Engineering. Wiley, Hoboken (2013)
Tsouknidas, A., Pantazopoulos, M., Katsoulis, I., Fasnakis, D., Maropoulos, S., Michailidis, N.: Impact absorption capacity of 3D-printed components fabricated by fused deposition modelling. Mater. Des. 102, 41–44 (2016)
Zou, R., Xia, Y., Liu, S., Hu, P., Hou, W., Hu, Q., Shan, C.: Isotropic and anisotropic elasticity and yielding of 3D printed material. Compos. B 99, 506–513 (2016)
Acknowledgments
This work was supported by a grant of the Romanian Ministry of Research and Innovation, CCCDI-UEFISCDI, project number PN-III-P1-1.2-PCCDI-2017-0224 / 77 PCDI/2018 within PNCDI III.
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Stănescu, ND., Beșliu-Gherghescu, ML., Tabacu, Ș. (2019). Use of Mini-Max Approximation for the Determination of the Dependency Between the Input and Output Parameters for the Automotive Parts Obtained by Fused Deposition Modeling (FDM). In: Burnete, N., Varga, B. (eds) Proceedings of the 4th International Congress of Automotive and Transport Engineering (AMMA 2018). AMMA2018 2018. Proceedings in Automotive Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-94409-8_45
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DOI: https://doi.org/10.1007/978-3-319-94409-8_45
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