The use of geometric uncertainty data in aero engine structural analysis and design

Abstract

A gas turbine disc has three critical regions for which lifing calculations are essential: the assembly holes or weld areas, the hub region, and the blade-disc attachment area. Typically, a firtree joint is used to attach the blades to the turbine disc instead of a dove-tail joint, which is commonly used for compressor discs. A firtree joint involves contact between two surfaces at more than one location which makes the joint more difficult to design. Large loads generated due to the centrifugal action of the disc and associated blades are distributed over multiple areas of contact within the joint. All of the contacts in a firtree joint are required to be engaged simultaneously when the blades are loaded. However, slight variations in the manufacture of these components can have an impact on this loading. It is observed that small changes in the geometric entities representing contact between the two bodies can result in variations in the stress distribution near contact edges and the notch regions. Even though manufacturing processes have advanced considerably in the last few decades, the variations in geometry due to these processes cannot be completely eliminated. Hence, it is necessary to design such components in the presence of uncertainties in order to minimise the variation observed in their performance. In this work, the variations in geometry due to the manufacturing processes used to produce firtree joints between a gas turbine blade and the disc are evaluated. These variations are represented in two different ways using measurement data of firtree joints obtained from a coordinate measuring machine (CMM): (i) the variation for the pressure angle in the firtree joint is extracted from a simple curve fit and (ii) using the same measurement data, the unevenness of the pressure surfaces is represented using a Fourier series after filtering noise components. A parametric computer aided design (CAD) model which represents the manufacturing variability is implemented using Siemens NX. Non-smooth surfaces are also numerically generated by assuming the surface profile to be a random process. Two- and three-dimensional elastic stress analysis is carried out on the firtree joint using the finite element code, Abaqus and the variations observed in the notch stresses with changing pressure angle are extracted. A surrogate assisted multiobjective optimisation is performed on the firtree joint based on the robustness principles. Kriging based models are used to build a surrogate for notch stresses and the non-dominated sorting genetic algorithm-II (NSGA-II) is implemented to perform a multiobjective optimisation in order to minimise the mean and standard deviation of the notch stresses. An iterative search algorithm that updates the Kriging models with equally spaced infill points from the predicted Pareto front is adopted. Finally, a new design of the firtree joint is obtained which has better performance with respect to the variation in the notch stresses due to manufacturing uncertainties.

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Identifiers

ORCID for Andy J. Keane: orcid.org/0000-0001-7993-1569

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