Turbine blade fir-tree root design optimisation using intelligent CAD and finite element analysis
Introduction
Over the last several decades, the engineering design world has been transformed by the introduction of massive computational power. Computers are now the principal tools for conceptual design, analysis, mock-up, and manufacture. CAD, analysis, mock-up and assembly checking are now completely carried out in a virtual environment and this process is being continuously updated [1]. In the engineering design community, the most notable changes lie in two aspects: CAD and analysis. Most companies use CAD and analysis software to deliver more reliable products in increasingly reduced time scales, but the pursuit of lower cost and shorter development time never stops because of the competitive world market.
The design process is a recursive one in which changes are often required during the later stages due to various factors arising as the design progresses, and design requirements often not only involve structure and functionality, but also cost, manufacture and environmental aspects. Traditional design processes typically treat these areas using different models and requirements are often described in different formats and different documents.
The use of finite element analysis has long become a common practice during the product development process, especially in the aerospace industry, where a large number of FE codes, including commercial packages and in-house codes are currently in use. The capability covers stress analysis, thermal and vibration analysis, as well as fatigue life estimates. Although most of these tools have user-friendly interfaces and powerful pre- and post-processing capabilities, the successful use of such tools requires experience in the field. These tools are now used at all stages of the design process from concept to detailed design.
The study and development of computer programs on mathematical optimisation algorithms has been a long term effort since the early 1960s and a large number of numerical algorithms are now available in the form of standard function library APIs together with some design exploration systems with built-in algorithms. OPTIONS [2] is such a system which provides a flexible framework for incorporating user codes ranging from very simple ones to complicated external software packages as well as more than 40 search algorithms and can be used either interactively or in batch mode.
The optimisation process typically starts with the parameterisation of the model and is then followed by a search process using different algorithms and strategies based on the evaluation of a measure of merit. Basically, there are three different types of parameterisation approach currently being developed for design optimisation in the engineering community [3]. The first is based on using the coordinates of the boundary grid points in a discretised domain as design variables, which is relatively easy to implement but makes it difficult to maintain a smooth geometry and the resulting optimised designs may be impractical for manufacture. The second is based on using a CAD system. Although the advantages of using a CAD system is obvious: smooth geometry, relatively small number of design variables, etc., it is difficult for traditional CAD systems to handle the variations of topology due to large perturbations in some dimensions. In addition, the underlying parameters describing the geometry are not normally available to calculate the sensitivities analytically. The third approach is similar to the morphing techniques used in computer sciences, and is termed free-form deformation, which is based on the idea of modelling the deformation rather than the base geometry. In this work, the second approach is adopted but the parametric modelling is performed using the design automation tool ICAD® from KTI [4]. The difference between ICAD and traditional CAD systems is that it can be used to generate parametric models based on various geometric features. Furthermore, non-geometric information can also be integrated into the model and used in the following analysis stages. The underlying geometric modelling engine used by ICAD makes possible the smooth transfer of geometry to analysis codes. The incorporation of ICAD and finite element codes into the search process gives the ability to carry out search based on high fidelity analysis results and to explore different geometric features using a relatively small set of parameters.
Section snippets
Overview
A fir-tree joint may be used in turbine structures to attach a blade to the rotating disk. Mechanical loads are transferred through the joint from the blade to the disk [5]. The overall aim of fir-tree structure optimisation program is to enable the designer to explore different candidate geometries at the preliminary stage, ranging from relatively simple designs to rather complex ones, at a reduced cost compared to using previous manual methods (such costs have often prevented the exploration
Geometry representation using ICAD
The product design process normally begins with the definition of requirements based on customer demands and goes from the conceptual design stage to the detailed design stage. Once the design specification is determined, the conceptual design stage starts with the implementation of the design in a computer environment followed by analysis to explore the feasibilities of candidates. Analysis plays an important role in investigating various design alternatives to determine the best design. It
Finite element analysis
The fir-tree joint used to hold a blade in place in a turbine structure is usually identified as a critical component which is subject to high mechanical loads. Most often the attachment is a multi-lobe construction used to transfer loads from blade to disk. It is generally assumed that there are two forms of loading which act on the blade, the primary radial centrifugal tensile load resulting from the rotation of the disk, and bending of the blade as a cantilever which is produced by the
Optimisation
Here two different optimisation problems were tackled using population based genetic algorithms (GAs) and gradient-based methods. One was to minimise the area outside of the last continuous radius of the turbine disc for the 2D case, which is proportional to the rim load by virtue of the constant axial length. This quantity is referred to as the fir-tree frontal area in the following sections. The number of teeth is treated as a design variable in this problem and the number of constraints is
Concluding remarks
The generative modelling facility provided by the ICAD system enables the rapid evaluation of different design alternatives in an engineering environment. Incorporating such capabilities into a FEA-based structural optimisation process has been shown to be an effective way to reduce design time scales and at the same time improve the quality of the end product. Other information such as a cost evaluation model or a manufacturing requirements model could be further included without sacrificing
Acknowledgements
This work was funded by the EPSRC under grant reference GR/M53158 and the University Technology Partnership for Design, which is a collaboration between Rolls-Royce, BAE SYSTEMS and the Universities of Cambridge, Sheffield and Southampton.
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