Modeling porous structures with fractal rough topography based on triply periodic minimal surface for additive manufacturing
Abstract
Purpose
The purpose of this paper is to develop a general mathematic approach to model the microstructures of porous structures produced by additive manufacturing (AM), which will result in fractal surface topography and higher roughness that have greater influence on the performance of porous structures.
Design/methodology/approach
The overall shapes of pores were modeled by triply periodic minimal surface (TPMS), and the micro-roughness details attached to the overall pore shapes were represented by Weierstrass–Mandelbrot (W-M) fractal representation, which was integrated with TPMS along its normal vectors. An index roughly reflecting the irregularity of fractal TPMS was proposed, based on which the influence of the fractal parameters on the fractal TPMS was qualitatively analyzed. Two complex samples of real porous structures were given to demonstrate the feasibility of the model.
Findings
The fractal surface topography should not be neglected at a micro-scale level. In addition, a decrease in the fractal dimension Ds may exponentially make the topography rougher; an increase in the height-scaling parameter G may linearly increase the roughness; and the number of the superposed ridges has no distinct influence on the topography. Furthermore, the synthesis method is general for all implicit surfaces.
Practical implications
The method provides an alternative way to shift the posteriori design paradigm of porous media to priori design mode through numeric simulation. Therefore, the optimization of AM process parameters, as well as the porous structure, can be potentially realized according to specific functional requirement.
Originality/value
The synthesis of TPMS and W-M fractal geometry was accomplished efficiently and was general for all implicit freeform surfaces, and the influence of the fractal parameters on the fractal TPMS was analyzed more systematically.
Keywords
Acknowledgements
This work is financially supported by the Nature Science Foundation of China (51505152, 51275177), the Fundamental Research Funds for the Central Universities (2015NM027), the Science & Technology Research Program of Guangdong (2016A030310409), the China Postdoctoral Science Foundation (2015M580720, 2016T90780) and the New Century Excellent Talents Program of China (NCET-12-0197).
Citation
Xu, Z., Wang, Q. and Li, J. (2017), "Modeling porous structures with fractal rough topography based on triply periodic minimal surface for additive manufacturing", Rapid Prototyping Journal, Vol. 23 No. 2, pp. 257-272. https://doi.org/10.1108/RPJ-09-2015-0121
Publisher
:Emerald Publishing Limited
Copyright © 2017, Emerald Publishing Limited