Development of advanced criteria for blade root design and optimization

In gas and steam turbine engines, blade root attachments are considered as critical components which require special attention for design. The traditional method of root design required high experienced engineers yet the strength of the material was not fully exploited in most cases. In the current thesis, different methodologies for automatic design and optimization of the blade root has been evaluated. Moreover, some methods for reducing the computational time have been proposed. First, a simplified analytical model of the fir-tree was developed in order to evaluate mean stress in different sections of the blade root and disc groove. Then, a more detailed two-dimensional shape of the attachment capable to be analyzed in finite element (FE) analysis was developed for dovetail and fir-tree. The model was developed to be general in a way to include all possible shapes of the attachment. Then the projection of the analytical model over the 2D model was performed to compare the results obtained from analytical and FE methods. This comparison is essential in the later use of analytical evaluation of the fir-tree as a reduction technique of searching domain optimization. Moreover, the possibility of predicting the contact normal stress of the blade and disc attachment by the use of a punch test was evaluated. A puncher composed of a flat surface and rounded edge was simulated equivalent to a sample case of a dovetail. The stress profile of the contact in analytical, 2d and 3d for puncher and dovetail was compared. As an optimizer Genetic Algorithm (GA) was described and different rules affecting this algorithm was introduced. In order to reduce the number of callbacks to high fidelity finite element (FE) method, the surrogate functions were evaluated and among them, the Kriging function was selected to be constructed for use in the current study. Its efficiency was evaluated within a numerical optimization of a single lob. In this study, the surrogate model is not used solely in finding the optimum of the attachment shape as it may provide low accuracy but in order to benefit its fast evaluation and diminish its low accuracy drawback, the Kriging function (KRG) was used within GA as a pre-evaluation of the candidate before performing FE analysis. Moreover, the feasible and non-feasible space in a multi-dimensional complex searching domain of the attachment geometry is explained and also the challenge of a multi-district domain is tackled with a new mutation operation. In order to rectify the non-continuous domain, an adaptive penalty method based on Latin Hypercube Sampling (LHS) was proposed which could successfully improve the optimization convergence. Furthermore, different topologies of the contact in a dovetail were assessed. Four different types of contact were modeled and optimized under the same loading and boundary conditions. The punch test was also assessed with different contact shapes. In addition, the state of stress for the dovetail in different rotational speed with different types of contact was assessed. In the results and discussion, an optimization of a dovetail with the analytical approach was performed and the optimum was compared with the one obtained by FE analysis. It was found that the analytical approach has the advantage of fast evaluation and if constraints are well defined the results are comparable to the FE solution. Then, a Kriging function was embedded within the GA optimization and the approach was evaluated in an optimization of a dovetail. The results revealed that the low computational cost of the surrogate model is an advantage and the low accuracy would be diminished in a collaboration of FE and surrogate models. Later, the capability of employing the analytical approach in a fir-tree optimization is assessed. As the fir-tree geometry has a higher complexity working domain in comparison to the dovetail, the results would be consistent for the dovetail also. Different methods are assessed and compared. In the first attempt, the analytical approach was adopted as a filter to select out the least probable fit candidates. This method could provide a 7\% improvement in convergence. In another attempt, the proposed adaptive penalty method was added to the optimization which successfully found the reasonable optimum with 47\% reduction in computational cost. Later, a combination of analytical and FE models was joined in a multi-objective multi-level optimization which provided 32\% improvement with less error comparing to the previous method. In the last evaluation of this type, the analytical approach was solely used in a multi-objective optimization in which the results were selected according to an FE evaluation of most fit candidates. This approach although provided 86\% improvement in computational time reduction but it depends highly on the case under investigation and provides low accuracy in the final solution. Furthermore, a robust optimum was found for both dovetail and fir-tree in a multi-objective optimization. In this trial, the proposed adaptive penalty method in addition to the surrogate model was also involved.