Structural Optimization of Fir-Tree Root and Groove for Turbine Blade With Splines and Genetic Algorithm

Abstract

The wide use of fir-tree root and groove in turbine structures prompts the expectation to find optimum configurations, which ensure that stresses are in the safe limits to avoid mechanical failure. To perform the optimization, the reasonable characterization of root configuration is required. The existing researches characterized the fir-tree root with straight line, arc or even elliptic fillet, then the parameters of these features were defined as design variables to perform root profile optimization. However, this feature-based optimization technique yields configuration which is only optimal under the feature assumption, the question why choose these feature and whether there is a better feature modeling technique is difficult to answer. In this work, instead of the feature-based method, spline curves technique is involved to characterize the root and groove configuration, and the horizontal coordinates of the control points are selected as design variables, which are modified in the vicinity of their initial values during optimization process. The objective function is to minimize the peak stress in the root and groove regions. With the Multi-island genetic algorithm, the optimal fir-tree root configuration can be obtained with better stress distributions and low stress concentrations. The proposed spline-based optimization approach may shed lights on the conceptual design of blade root and can be easily extended to other industrial equipment design.

Uncertainty and global sensitivity analysis of bladed disk statics with material anisotropy and root geometry variations

“…There are articles in the literature that deal with the optimization of the fir tree root joint geometry with the objective of reducing the stresses in the joint. [16][17][18][19][20][21] Random errors in manufacturing process introduce variability in the geometry of the blade root and the disk slots. Due to the variability in blade and disk geometry within the tolerance limits, the contact area at joints could be higher or lower than that of the nominal design geometry.…”

“…Random forest methods have been applied with varying degree of success to regression and classification problems arising in different fields ranging from fluid flow modeling 29 to medical prognosis. 17 Ling and Templeton 30 investigated the use of three different data-driven algorithms including RF and support vector machines 31 to identify regions in a fluid flow where the inaccuracy of Reynolds-averaged Navier-Stokes (RANS) models is high. They concluded that data-driven algorithms provide a substantial improvement over conventional RANS error detection methods and showed the performance of RF to be superior compared with that of the other algorithms used.…”

“…Meguid et al studied the effect of variation in certain key geometric features of the fir tree, such as the number of teeth, flank angle, and flank length, on von‐Mises stresses on disk slot. There are articles in the literature that deal with the optimization of the fir tree root joint geometry with the objective of reducing the stresses in the joint …”

“…The performance of the RF model is validated using data in the test set. Random forest methods have been applied with varying degree of success to regression and classification problems arising in different fields ranging from fluid flow modeling to medical prognosis . Ling and Templeton investigated the use of three different data‐driven algorithms including RF and support vector machines to identify regions in a fluid flow where the inaccuracy of Reynolds‐averaged Navier‐Stokes (RANS) models is high.…”

Design optimization of aero-engine turbine blade and disc fixing

“…In the second step, after identifying the most sensitive design variables, several optimization methods such as the NSGA-II non-dominated sorting genetic algorithm, Downhill Simplex and an evolutionary optimization algorithm were used and compared. Deqi Yu et al, 7 used the Multi-island genetic algorithm in order to obtain the optimal fir-tree root with better stress distributions and low stress concentrations. A single objective Genetic Algorithm (GA) was used by Alinejad et al, 8 in order to find the optimum fir-tree shape having minimum von-Mises stress.…”