Use of fractal curves for reducing spatial thermal gradients and distortion control

Abstract

In Additive Manufacturing, the desired geometry is achieved by gradual and sequential addition of material. This evolutionary nature of AM, which facilitates the fabrication of complex geometries, also results in distinctive thermal evolution for each unit of material added. An asymmetry in the heat gradients and the resulting thermal imbalance can result in residual stresses and distortions. This thermal imbalance can be mitigated by controlling the spatial spread of the heat inside the system. The aim of the current work is to delve into the fundamental behavior of heat gradients and look at ways to mitigate these gradients in a manner that is applicable to a wider spectrum of setups and scales. Hence, the focus of the current work is on regulating the area-filling paths (scan patterns) to control the spatial distribution of heat. It is hypothesized that fractal area-filling curves, like Hilbert, due to their continuous and recursive nature, can help in better heat distribution and reduce residual stresses and distortions. This concept is actualized for the Wire and Arc Additive Manufacturing (WAAM) process through simulation and experimental validation. Three different geometries and each at three different dimensional scales were taken up for study. For each of these geometries, the area-filling paths were generated in Zigzag, Contour (out-to-in) and Hilbert area-filling methods. Based on the data extracted from the simulation of these cases in Simufact software, the Hilbert pattern was found to have minimal thermal gradients in all cases. This favorable behavior of Hilbert was further corroborated with the help of experiments using weld deposition of the geometries. For the Hilbert area-filling, the distortions are reduced to values 41 % - 53 % for scaled-up, 53 % - 63 % for unscaled and 80 % - 93 % for scaled-down. These results validate the correlation between the differential temperature and distortion and the ability of fractal curves like the Hilbert curve for achieving better thermal distribution, decreasing the differential temperature.