Deposition Volume Compensation for Enhanced Shape Fidelity in Nested Printing

Nested printing, a special type of embedded printing, enables the fabrication of multilayered enclosed structures, in particular those resembling biological organs. As with any printing process, shape fidelity in nested printing is of great importance to dimensional accuracy, structural integrity, and/or functionality of 3D-printed parts. Particularly, the shape fidelity may be compromised due to the upflow and the additional volume introduced by internal depositions, and the latter is not well studied yet and calls for robust mitigation approaches. This study aims to establish a B-spline function-based three-dimensional (3D) freeform compensation method to offset the effect of internally deposited volumes in internally nested structures during nested printing. Particularly, printed nested structures are visualized using image-based segmentation and reconstruction, shape fidelity is assessed by measuring deviations between reconstructed and designed models using 3D structural similarity analysis, and a distortion field and a corresponding compensation field are approximated using a B-spline function-based method, resulting in a compensated 3D model for final nested printing. This compensation method reduces the mean printing error from 9.35% to 2.02% for the first enclosing layer and from 17.59% to 0.47% for the second enclosing layer, respectively, for a canonical nested structure. Further, the demonstration case of a 3D brain limbic system model shows a reduced mean printing error from 10.67% to 1.40% for the enclosing white matter region. The compensation-based mitigation strategy using the B-spline function effectively enhances shape fidelity during nested printing.