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Laser power based surface characteristics models for 3-D printing process

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Abstract

Selective laser melting (SLM) is one of the important 3-D Printing processes that builds components of complex 3D shapes directly from the metal powder. It is widely used in manufacturing industries and is operated on significant amount of laser power drawn from the electric grid. The literature reveals that the properties such as surface roughness, waviness, tensile strength and dimensional accuracy of an SLM fabricated parts, depend on the laser power and can be improved by its appropriate adjustment. Determination of accurate values of laser power and the other inputs could lead to an improvement in energy efficiency and thus contributing to a clean and healthy environment. For determining the accurate value of laser power in achieving the required surface characteristics, the formulation of generalized mathematical models is an essential pre-requisite. In this context, an artificial intelligence approach of multi-gene genetic programming (MGGP) which develops the functional expressions between the process parameters automatically can be applied. The present work introduces an ensemble-based-MGGP approach to model the SLM process. Experiments on the SLM process with measurement of surface characteristics, namely surface roughness and waviness, based on the variations of laser power and other inputs are conducted, and the proposed ensemble-based-MGGP approach is applied. Statistical evaluation concludes that the performance of the proposed approach is better than that of the standardized MGGP approach. Sensitivity and parametric analysis conducted reveals the hidden relationships between surface characteristics and the laser power, which can be used to optimize the SLM process both economically and environmentally.

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Acknowledgments

The study was supported by Nanyang Technological University’s funding, Reference Number M060030008.

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Authors and Affiliations

  1. School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore

    A. Garg & Jasmine Siu Lee Lam

  2. Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong

    M. M. Savalani

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  1. A. Garg
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  2. Jasmine Siu Lee Lam
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Correspondence to M. M. Savalani.

Appendix

Appendix

$$\begin{aligned}&\textit{Surface roughness}_{\textit{MGGP}} =8.8498+( {0.015232})\nonumber \\&\quad *\,( ( {\hbox {x}3} )\,*\,( ( \hbox {tan}( ( \hbox {tan}({\hbox {x}2} ) )\,*\,( {\hbox {x}1} )))\,*\,(( \hbox {tan}( {\hbox {x}2} ))\,*\,({\hbox {x}1})))) \nonumber \\&\quad +\,( {-4.3936} )\,{*}\,((\hbox {tan}(\hbox {sin}(( \hbox {tan}({\hbox {x}2} ))\,{*}\,( {\hbox {x}1} ))))\,{*}\,( ( (\hbox {cos}( {\hbox {x}3} ))\nonumber \\&\quad {*}\,({\hbox {x}3} ))\,{*}\,( \hbox {plog}(\hbox {tan}(\hbox {x}3)))))+(-0.012043)\,{*}\,((\hbox {tan}(\hbox {x}3))\nonumber \nonumber \\&\quad {*}\,(( \hbox {x}3)\,{*}\,( (\hbox {tan}( {\hbox {x}2} ) )\,{*}\,( {\hbox {x}1} ) ) ) )+( {0.036929})\,{*}\,(\hbox {tan}(((({\hbox {x}2}) \nonumber \\&\quad -\,( {\hbox {x}1} ))+( ( {( {-5.249071})} )-( {\hbox {x}1} )))\,{*}\,( ( {\hbox {x}2} )\nonumber \\&\quad -\,({\hbox {tan}( {\hbox {tan}( {\hbox {x}2} )} )}) )))+( {-0.39776} )\,{*}\,( \hbox {tan}( \hbox {x}2 ) ) \nonumber \\&\quad +\,( 9.888\hbox {e}-005 )\,{*}\,(( {\hbox {x}3} )\,{*}\,(( ( \hbox {tan}( {\hbox {x}2} ) )\nonumber \\&\quad {*}\,( \hbox {sin}( \hbox {plog}( {( {8.353597} )} ) ) ) )\,{*}\,( {\hbox {tan}( {\hbox {x}2} )} ))) \nonumber \\&\quad +\,( {-0.095928} )\,{*}\,( \hbox {tan}(( {\hbox {x}3} )\,{*}\,( ( {\hbox {x}2} )-( {\hbox {x}3} ) ) ) )\nonumber \\&\quad +\,( {0.064227} )\,{*}\,((( {\hbox {tan}( {\hbox {x}2} )} ) \,{*}\,( {\hbox {x}1} ))\,{*}\,( {\hbox {tan}( {\hbox {x}2} )} )) \end{aligned}$$
(5)
$$\begin{aligned}&\textit{Waviness}_{\textit{MGGP}} =-136.8083+(-2.4736)\,{*}\,(\hbox {x}3)\nonumber \\&\quad +\,(155.1688 )\,{*}\,(\hbox {cos}(\hbox {tanh}( \hbox {tan}(( \hbox {x}2)-(\hbox {x}1)))))\nonumber \\&\quad +\,({-0.07331})\,{*}\,(({\hbox {x}2})\,{*}\,(\hbox {sin}({\hbox {x}3})))+( {6.4672} ){*}( ( {\hbox {x}1} )\nonumber \\&\quad {*}\,( {\hbox {x}3} ))+( {22.7613} )\,{*}\,(\hbox {cos}((({\hbox {x}1})\,{*}\,( ( {\hbox {x}2} )\nonumber \\&\quad -\,( {\hbox {sin}( {\hbox {x}3} )} ) ))+( {\hbox {x}1} )))+( {117.5742} )\,{*}\,( \hbox {tanh}(( {\hbox {x}3} )\nonumber \\&\quad {*}\,( {\hbox {x}1} ) ) )+( {78.3211} )\,{*}\,( {\hbox {x}1}) +( {-0.1337} )\,{*}\,( {\hbox {x}2} ) \end{aligned}$$
(6)
$$\begin{aligned}&\textit{Surfaceroughness}_{\textit{EN}{\text {-}}{} \textit{MGGP}} =8.6796+( {0.27771} )\nonumber \\&\quad {*}\,(( ({\hbox {x}1} )\,{*}\,( {( {( {\hbox {x}1} )\,{*}\,( {\hbox {tan}( {\hbox {x}2} )} )} )\,{*}\,( {\hbox {x}3} )} ) ) \,{*}\,(\hbox {cos}(( ({\hbox {x}1} )\,{*}\,( \hbox {tan}( {\hbox {x}2} )))\nonumber \\&\quad {*}\,( {\hbox {x}3} ))))+( {10.578} )\,{*}\,( \hbox {sin}( ( ( {\hbox {x}1} )\,{*}\,( {\hbox {tan}( {\hbox {x}2} )} ) )\,{*}\,({\hbox {tan}( {\hbox {x}2} )} ) ) )\nonumber \\&\quad +\,( {0.0058965} )\,{*}\,( {\hbox {x}2}) +( {8.0947} )\,{*}\,( \hbox {sin}(( {( {\hbox {x}1} )\,{*}\,( {\hbox {x}1} )} )-( ( {\hbox {x}3} )\nonumber \\&\quad +\,( {( {-4.029785} )} ) ) ) )+( {2.5051} )\,{*}\,(( {\hbox {x}1})\nonumber \\&\quad {*}\,( {\hbox {tan}( {\hbox {x}2} )} ))+( {-1.1768} )\,{*}\,( ( ( {\hbox {x}1} ) \,{*}\,( {\hbox {x}3} ) ){*}( \hbox {tan}( ( {\hbox {x}1} )\nonumber \\&\quad {*}\,( {\hbox {tan}( {\hbox {x}2} )} ) ) ) )+( {6.9443} )\,{*}\,( ( {\hbox {cos}( {\hbox {x}3} )} )\,{*}\,( \hbox {tan}(( {\hbox {x}1} )\nonumber \\&\quad {*}\,( {\hbox {tan}( {\hbox {x}2} )} ) ) ) )\quad +\,( {0.0061773} )\,{*}\,( {( {\hbox {tan}( {\hbox {x}2} )} )\,{*}\,( {\hbox {x}3} )} ) \end{aligned}$$
(7)
$$\begin{aligned}&\textit{Waviness}_{\textit{EN}{\text {-}}{} \textit{MGGP}} =1092.6173+( {0.11925} )\nonumber \\&\quad {*}\,( \hbox {tan}( ( {\hbox {tan}( {\hbox {x}3} )} )+( ( {\hbox {x}2} )-( {\hbox {x}1} ) ) ) )+( {23.4796} )\,{*}\,(\hbox {tan}(( {\hbox {x}3} )\nonumber \\&\quad +\,( {\hbox {x}1} )))+( {-1.0985} )\,{*}\,( {\hbox {x}3} )+( {-418.4781} )\nonumber \\&\quad {*}\,( \hbox {plog}( \hbox {plog}( ( {\hbox {x}2} )\,{*}\,( {\hbox {tan}( {\hbox {x}3} )}))))+( {-201.3874} )\nonumber \\&\quad {*}\,( \hbox {tan}( {\hbox {cos}( {\hbox {cos}( {\hbox {sin}( {( {\hbox {x}2} )-( {\hbox {x}1} )} )} )} )} ) ) +({-30.4952} )\,{*}\,( {\hbox {tan}( {\hbox {x}3} )})\nonumber \\&\quad +\,( {-31.5096} )\,{*}\,( {\hbox {cos}( {\hbox {x}2} )} )+( {45.6679} )\,{*}\,( {\hbox {plog}( {\hbox {x}1} )} ) \end{aligned}$$
(8)

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Garg, A., Lam, J.S.L. & Savalani, M.M. Laser power based surface characteristics models for 3-D printing process. J Intell Manuf 29, 1191–1202 (2018). https://doi.org/10.1007/s10845-015-1167-9

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