A mathematical surface roughness model for objects made by material jetting

This study aims to develop a mathematical model of the surface roughness of objects produced by multi-jet printing at sub-zero temperatures. Previous research on Sub-zero Additive Manufacturing (SAM) has described the “Ice line Model” for single jet dispensing, which accounts for individual droplet geometry but ignores the staircase effect, which is a key cause of roughness in 3D printed products. The “Spherical Cap Model” for Stratasys’ PolyJet process considers the staircase effect but does not consider individual droplet shape. The model presented in this paper addresses individual droplets in the same way as the ice line model, and the staircase effect in the same way as the spherical cap model, thus eliminating the drawbacks of both. Droplets per inch (DPI) and surface inclination are the two main criteria that influence surface roughness. Therefore, the sample objects were printed using a PolyJet-like custom-made Sub-zero Additive Manufacturing (SAM) machine with two DPI settings, 360 and 720, and ten different surface inclinations (0°, 10°, 20°, 30°, 40°,50°, 60°, 70°, 80°, 90°). The surface roughness of the sample parts was measured and compared to theoretical values calculated using a mathematical model. The proposed mathematical model is consistent with the experimental results and is found to predict the surface roughness values more accurately than previously existing models. A complete surface roughness model is presented in this paper for the multi-jet-based AM processes.