A numerical formalism towards finding a good component orientation in laser powder bed fusion

Abstract

• Mathematical formulation of several of objectives considered when deciding how to orient a part during LPBF. • Consideration of printing cost as a metric affecting orientation decisions. • Reduction of complex distortion and residual stress results to a representative variable manageable by multi-objective optimization. • Discontinuity in distortion and residual stress results make it difficult to use machine learning tools. Monte-Carlo optimization is not as sensitive to discontinuities. • The frequency of distortion computations is analyzed to achieve reasonably reliable predictions with least possible computational effort. Several manufacturing constraints and objectives are considered when choosing a build orientation for laser powder bed fusion (LPBF) parts. Some of them are inversely proportional to one another making it necessary to formalize an optimization scheme with weighting factors enabling engineers to decide which of them is most relevant for the application under consideration. Several of the considered cost functions are quick to calculate (e.g. down skin area). The reduction of residual stresses and distortion are on the other hand computationally intensive and are not easily considered in an optimization scheme. Solution sampling in 3 angular directions is therefore utilized to create a response surface describing the part distortion in arbitrary orientations. The response surface accuracy is studied before applying it together with 7 other cost functions within a multi-objective Monte-Carlo optimization scheme.