Statistical and dynamic model of surface morphology evolution during polishing in additive manufacturing

Many industrial components, especially those realized through 3D printing undergo surface finishing processes, predominantly, in the form of mechanical polishing. The polishing processes for custom components remain manual and iterative. Determination of the polishing endpoints, i.e., when to stop the process to achieve a desired surface finish, remains a major obstacle to process automation and in the cost-effective custom/3D printing process chains. With the motivation to automate the polishing process of 3D printed materials to a desired level of surface smoothness, we propose a dynamic model of surface morphology evolution of 3D printed materials during a polishing process. The dynamic model can account for both material removal and redistribution during the polishing process. In addition, the model accounts for increased material flow due to heat generated during the polishing process. We also provide an initial random surface model that matches the initial surface statistics. We propose an optimization problem for model parameter estimation based on empirical data using KL-divergence and surface roughness as two metrics of the objective. We validate the proposed model using data from polishing of a 3D printed sample. The procedures developed makes the model applicable to other 3D printed materials and polishing processes. We obtain a network formation model as a representation of the surface evolution from the heights and radii of asperities. We use the network connectivity (Fiedler number) as a metric for surface smoothness that can be used to determine whether a desired level of smoothness is reached or not.