Improving the directional solidification of complex geometries through taper addition

The Niyama criterion identifies centerline shrinkage in simulations of directionally solidifying alloys. Adding taper to the casting surface is an effective strategy to eliminate regions of critical Niyama criterion and improve the soundness in castings. However for complex geometries, there may not be an intuitive taper solution. The Niyama criterion will validate these complex tapers but not guide the design of that taper. When evaluated near the end of solidification, a thermal criterion such as the cooling rate on the surface of the casting can serve as an identification of efficient areas to taper. The cooling rate is used to calculate an effective depth (ED) which is representative of the half thickness of the underlying section. The spatial gradient of the effective depth (EDG) can be correlated to the Niyama criterion at the casting's centerline to predict the magnitude of existing taper. The EDG can then be used as a constraint for a minimal taper optimization. The EDG was calculated on two flat plates, one with and without taper, to show that this is a viable methodology for taper identification. The method is also performed on a real axle housing with know dispersed porosity to demonstrate its usefulness on three-dimensional castings.