Optimal trajectory smoothing for direct energy deposition additive manufacturing processes

In free form additive manufacturing processes (e.g., metal blown powder, glass filament, ceramic paste extrusion), part quality depends on both the rate at which the part is built and where material is deposited. This creates a natural conflict between these two criteria at locations where the curvature of the programmed path is small, such as corners, because at these locations it is not possible to precisely follow the path without changing acceleration and, hence, varying the part build rate due to the variation in path velocity. In some additive manufacturing processes it is not possible to easily vary the material feed rate to maintain a constant part build rate when path velocity varies; thus, uneven material deposition occurs. In this work an optimal trajectory smoothing methodology is created that formulates the path following problem as an optimal dynamic system boundary value problem. The methodology naturally allows a trade-off between path following error and velocity error and is experimentally applied in a blown powder direct metal deposition additive manufacturing process. The results show that path and velocity errors increase as the corner angle decreases and the velocity entering the corner increases; however, they can be decreased by increasing the corner's leg length. Further, as the weight on velocity error increases, the velocity error, excess deposited material, and total print time decrease asymptotically while path error increases asymptotically.