An unconstrained approach to blank localization with allowance assurance for machining complex parts

In machining large complex parts with critical stock allowance, even small deviations in the blank parts or slight inadequacy in the fixturing may result in local shortage of material (i.e., insufficient stock allowance). This paper presents an optimal localization algorithm that aligns the measured points from a blank part with the nominal model to assure the weakest allowance area with as much material to be cut as possible. Instead of exploiting extra constraints to force the allowance at each point larger than a specific value, which is a popular strategy for allowance assurance in the previous localization algorithms, we formulate the blank localization problem as an unconstrained max-min problem. To deal with the unsmoothness exhibiting in the max-min objective function, a method based on the entropy optimization principle is adopted to convert the non-differential objective function to an unconstrained differential one, which can be efficiently solved using the conventional Quasi-Newton algorithms. The unconstrained optimization result finally gives rise to localization with the maximum allowance margin. For the blank parts that the material shortage is inevitable, the method can still efficiently achieve reasonable localization results, which confine the material shortage to a least extent. The proposed method is easy to be implemented and works well for both sparse sample points and dense-scanned points. Case studies included justify the superiority of the proposed scheme over the existing non-linear constrained optimization solutions.