Statistical Modelling and Optimization of Directional Volumetric Error in FDM Prototyping

Volumetric error (VE) is a critical source of dimensional inaccuracy in fused deposition modeling (FDM), and its contribution can vary significantly along different directions of a fabricated component. This study presents a response surface methodology (RSM)-based approach for modeling and optimizing the directional contribution to volumetric error in FDM-fabricated components. ABS-M30 specimens were fabricated using a Stratasys Fortus 400mc system according to a 32-run central composite design (CCD). Five FDM process parameters—build orientation (0–60°), raster width (0.4064–0.8064 mm), raster angle (0–60°), air gap (0–0.508 mm), and contour width (0.4064–0.8064 mm)—were investigated. Directional volumetric errors were evaluated independently along the X-, Y-, and Z-directions, corresponding to the length, width, and thickness of the specimens, respectively. Second-order response surface models were developed and statistically refined by eliminating insignificant terms using an F-value threshold of 1.5. All final models were statistically significant (p < 0.0001), with coefficients of determination (R 2 ) of 0.9970, 0.9946, and 0.9978 for the X-, Y-, and Z-directional errors, respectively. Air gap was identified as the most influential parameter, with increasing air gap causing substantial changes in volumetric error, while increasing raster width generally reduced the magnitude of error. Significant two-factor interactions further demonstrated the coupled nature of the process parameters and their direction-dependent effects. Multi-response optimization yielded an optimum combination of build orientation of 38.77°, raster width of 0.7874 mm, raster angle of 7.74°, air gap of 0.0478 mm, and contour width of 0.7715 mm, with predicted directional errors approaching zero. The findings demonstrate that coordinated selection of FDM process parameters can effectively control directional volumetric error and improve dimensional accuracy.