Fast solution strategy for transient heat conduction for arbitrary scan paths in additive manufacturing

A unique and efficient semi-analytic method is presented for quickly predicting the three-dimensional thermal field produced by conduction from a heat source moving along an arbitrary path. A Green's function approach is used to decouple the solution at each time step into the analytical source contribution and a conduction contribution. The latter is solved numerically using efficient Gaussian convolution algorithms. This decoupling allows for boundary conditions on side boundaries to be satisfied numerically and lowers computational expenses by allowing calculations to be localized around the heat source. The thermal field resulting from arbitrary scan paths is constructed using analytical solutions for elementary linear segments. With focus on efficiency, a novel approach is used to store the calculated analytical line solutions for reuse on multiple other path segments. The results of various scan patterns are presented and successfully verified against finite element simulations. The computational times of predictions are shown to be faster than the corresponding finite element simulation by an order of magnitude with less than 1% average error. Given its ability to quickly predict the thermal history and changes in melt pool geometry due to arbitrary scan paths, this method provides a potentially powerful tool for exploration and optimization of laser powder bed fusion processes.