Reduction of the design space to optimize blade fir-tree attachments

The blade attachment, both dovetail or fir-tree, transfers the centrifugal load from the blade to the disc, generating high mean and peak stresses in notches as well as on contact surfaces. Hence, the strength of the attachment is one of the main concern of the designers for improving the performance of the engine and several optimization procedure have been put forward to minimize the state of stress in the attachment for a given centrifugal load. The optimization process is generally driven by a parametric model. The selection of the proper parameters and their variation ranges represent one of the main issues for the process to converge in a reasonable amount of time. Simulation methods and optimization algorithms have been improved a lot in the past years. Nevertheless, the computational effort of the finite element analysis involved in the optimization procedure of complex geometries remains a critical task. Moreover, an accurate evaluation of the local contact stresses is highly dependent on the mesh refinement, increasing the computing time of the whole optimization process. Moreover, a multi-objective optimization, in addition to robustness design approach, is the designer tool to improve the attachment performance. The searching domain reduction of the optimization process improves the computational performance reducing the convergence time of the solution. To achieve this goal, a preliminary selection of the design space has been performed by means of an analytical approach. This paper describes a new design criterion based on one dimensional approach. The criterion has been implemented in an in-house tool that takes faster decisions, if compared with a two or a three dimensional model, about the number of possible feasible solutions. During the geometrical optimization phase of the blade fir-tree attachment, in which a parametric model is used, the authors try to handle the geometrical non-feasibility with a combination of Latin Hypercube Sampling (LHS) and an adaptive penalty method. The optimization is done via the genetic algorithm and the computational time of the reduced domain is compared with the original one.