Allowance optimization for forged Pelton turbine bucket based on point cloud registration and constrained variance minimization

The blank for Pelton turbine buckets is mainly manufactured by forging which usually leads to uneven machining allowances. Under traditional processes, uneven removal of excess material from rough blanks can easily cause non-uniform release of residual stresses, resulting in deformation exceeding tolerance limits. To address this issue, this study proposes a constrained variance minimization approach for blank allowance optimization. The point cloud data of the deformed blank is reduced via voxel down-sampling while preserving critical geometric features through farthest-point sampling. The same preprocessing is applied to the nominal CAD model. Initial alignment between the scanned blank and the CAD model is achieved using PCA-based coarse registration, followed by a refined iterative closest point (ICP) algorithm incorporating Truncated Least Squares (TLS) for enhanced accuracy. To handle the common issue of the pre-aligned point cloud only partially enclosing the theoretical model, normal vector estimation and feature surface segmentation are introduced to identify distinct machining regions with specific allowance requirements. A constrained variance minimization algorithm is then applied to optimize the allowance distribution, ensuring both uniformity and sufficiency in critical areas. The proposed method improves material utilization and reduces manufacturing costs. Furthermore, the framework demonstrates strong potential for extension to high-performance machining of aerospace monolithic components—such as titanium integral blade rotors (blisks) and turbine casings—where similar challenges with residual stress and strict allowance control are prevalent. Adapting this technique could significantly enhance manufacturing efficiency for high-value manufacturing without compromising part integrity.