CAD Based Shape Optimization for Gas Turbine Component Design

Struct Multidisc Optim (2010) 41:647659DOI 10.1007/s00158-009-0442-9

INDUSTRIAL APPLICATION

CAD based shape optimization for gas turbine component designDjordje Brujic Mihailo Ristic Massimiliano Mattone Paolo Maggiore Gian Paolo De Poli

Received: 8 July 2009 / Accepted: 12 September 2009 / Published online: 12 November 2009c Springer-Verlag 2009

Abstract In order to improve product characteristics, engi-neering design makes increasing use of Robust Design andMultidisciplinary Design Optimisation. Common to bothmethodologies is the need to vary the objects shape and toassess the resulting change in performance, both executedwithin an automatic loop. This shape change can be realisedby modifying the parameter values of a suitably parame-terised Computer Aided Design (CAD) model. This paperpresents the adopted methodology and the achieved resultswhen performing optimisation of a gas turbine disk. Ourapproach to hierarchical modelling employing design tablesis presented, with methods to ensure satisfactory geome-try variation by commercial CAD systems. The conductedstudies included stochastic and probabilistic design optimi-sation. To solve the multi-objective optimisation problem, aPareto optimum criterion was used. The results demonstratethat CAD centric approach enables significant progresstowards automating the entire process while achieving ahigher quality product with the reduced susceptibility tomanufacturing imperfections.

Keywords Design optimisation Robust design Parametric CAD modelling Gas turbine

D. Brujic (B) M. RisticImperial College London, London, UKe-mail: [email protected]

M. Mattone P. MaggiorePolitecnico di Torino, Turin, Italy

G. P. De PoliAvio SpA, Avio, Italy

1 Introduction

Engineering design makes increasing use of methodolo-gies such as Multidisciplinary Design Optimisation (MDO)and Robust Design (RD). In this paper their applicationin situations where the geometry of a component is tobe optimised in order to achieve certain goals is consid-ered. Geometry optimisation requires variation of the objectshape and assessment of the resulting change in the perfor-mance (Haslinger and Mkinen 2003). This is common toboth MDO and RD methodologies.

MDO is concerned with achieving a design that simul-taneously satisfies the requirements and optimises the per-formance in different disciplines. In aerospace engineeringthis may involve optimisation of parameters by consid-ering the combined structural, thermal and aerodynamicperformance.

Robust design on the other hand is fundamentally con-cerned with minimizing the effect of uncertainty or variationin the design parameters without eliminating the source ofthat uncertainty or variation (Kalsi et al. 2001; Apley et al.2006). In other words, a robust design is less sensitiveto variations in uncontrollable design parameters than thetraditional optimal design. Robust design has found manysuccessful applications in engineering and is continuallybeing expanded to different design phases. Although robustdesign has been traditionally applied in manufacturing therehas been research recently into applying these techniquesto make the design conceptually robust. The importantroles of modelling and calculation of robustness in a mul-tidisciplinary design environment is discussed in Marczyk(2000).

Realisation of MDO and RD processes inevitablyrequires close integration of functions such as geomet-ric design, engineering analysis (e.g. finite element) and

648 D. Brujic et al.

Fig. 1 Gas turbine disc

optimisation algorithms, (Bennett et al. 1998; Madetojaet al. 2006). Such functions are today extensively supportedby commercial software packages which may be used incombination to achieve maximum benefits. Modern CADsystems (e.g. Catia, Pro/E, Unigraphics) are used as thecentral tool for creating and maintaining product definitionthroughout its lifecycle. They provide a rich set of toolsfor creation and management of geometry, ranging fromparts to complex assemblies, databases of material prop-erties and, increasingly, encapsulation of specialist designmethods (e.g. UG Knowledge Fusion). Analysis packages(e.g. MSc Software, Ansys) include extensive pre- andpost-processing functions together with solvers dedicatedto specific disciplines. Optimisation methods may involveNewton or quasi-Newton type algorithms, while evolution-ary and probabilistic methods are increasingly used. Suchmethods may be implemented using bespoke code, whilethere is also an increasing number of software packagesoffering such functionality (e.g. modeFrontier, MSC/RobustDesign, iSIGHT).

The optimisation process is characterized by significanthuman involvement needed to develop the CAD model, togenerate the analysis models, to execute the analysis codeand finally to examine the output and make decisions. Sincethe analysis task may require a considerable computationaltime, automation of the overall procedure is the key torealising higher design productivity. Thus the design practi-tioners are increasingly interested in methods for integration

of such software into an automatic optimisation loop inorder to perform difficult optimisation tasks involving multi-ple design objectives and constraints. An important practicalissue is that many of the relevant software tools, especiallyCAD, are primarily intended for standalone interactive useand their integration into an automatic loop demands specialattention.

This paper presents results of the research that has beenconducted under the auspices of the EU Framework 6project VIVACE (Value Improvement through a VirtualAeronautical Collaborative Enterprise)a consortium ofabout 70 European aerospace manufacturers and academicinstitutions. Among the many aspect of this large project,the central theme has been the provision of methods andtools to enable close integration between various disciplinesand tools involved in modern aeroengine design aimed atmeeting the overall design targets such as thrust, weight andservice life. These include thermal cycle analysis, aerody-namic performance, vibration analysis of the whole engine,coupled with structural, thermal and fatigue life analysis ofindividual components. Robustness of the final design inthe context of multidisciplinary design optimisation is anoverriding requirement.

The design case considered here involves shape optimisa-tion of a high pressure gas-turbine disc of an aircraft engine(Fig. 1). The high pressure disk is treated as a generic exam-ple of a large class of complex objects that are representedas solids of revolution and/or extrusions. In an aero engine

CAD based shape optimization for gas turbine component design 649

such components do not directly affect the gas flow butare critical for the overall weight, fatigue life and vibra-tion characteristics. Disk design involves two main aspectsthat are addressed independently. The first is the design ofthe disc shape, aimed at minimising the weight while max-imising the life by maintaining the stresses in critical areaswithin the prescribed limits. The second is the optimisationof the disk slot and blade root, which provides the inter-face between the two components. In both cases the overallobjective is to achieve an optimal design while ensuring thatthe design is robust in the presence of uncertainties.

2 Geometric modelling for shape optimisation

There are, basically two approaches to CAD and CAEintegration (Lee 2005):

CAE-centric approach CAD-centric approach

In the CAE-centric process, engineering analyses areperformed initially to define and refine a design conceptusing idealized analysis models before establishing theCAD model of the product. The design process usuallystarts with the simplest idealisations of a solid geometryand progresses to more complex ones. CAE geometry typi-cally involves lines or sheets, from which the 3D model maybe subsequently generated by adding detail and dimensionalinformation. Techniques proposed to carry out dimensionaladdition and to create solids from abstract models involvesheet thickening, offsetting, and skeleton re-fleshing oper-ations (Lee et al. 2005), but this is not well supported bycurrent systems. CAE geometry cannot be easily used toconstruct a CAD model, nor other instances of CAE geom-etry at different levels of abstraction. In practise each suchnew model needs to be re-created from scratch.

In the CAD-centric approach, the design is captured ini-tially in a CAD system, while the CAE model is derivedfrom that. Since the CAE model usually involves ideal-isation of the detailed product geometry, many aspectsof its creation are supported by the parametric modellingparadigm adopted by the modern CAD systems. For exam-ple, simplification of a given solid can often be effectivelyachieved simply by turning off certain features in the modeltree. In other situations however, preparation of the CAEmodel may involve more complex operations in CAD. Forexample the CAE model may be represented by a 2Dsection involving more than one part, which is not availablethrough simple de-featuring and requires explicit geometricoperations. Such construction can be performed using avail-able CAD functionality, automated using built-in scriptinglanguages and applied automatically on a family of parts.

Both of these approaches require considerable effort tocreate and consistently maintain different models for oneproduct, but the CAD-centric approach was considered tooffer a number of important advantages. First, it is con-sidered to provide an easier and more natural integrationwith engineering analysis, especially in situations involv-ing multiple disciplines and complex assemblies. Second, iteliminates any representation related restrictions on allow-able geometry changes, which can then be tailored forhigher fidelity analysis. Finally, the approach will in thelonger term strongly benefit from the continuing advancesin CAD functionality, leading to improved productivity.

In this way CAD becomes the source and repository forall relevant geometric information, including the definitionof geometric parameters that are the variables in the opti-misation process. The geometric definition can be readilyaugmented with discipline-specific engineering informationsuch as material properties and boundary conditions. Con-straints and influences arising in one discipline and affectingother disciplines are also easier to manage in a complexdesign scenario.

The drawbacks of this method include the complexity ofgeometry generation script. Furthermore, it was recognisedthat existing CAD systems do not robustly support paramet-ric modelling, posing issues for implementation of varia-tional modelling in an automated fashion. Existing practicesin parametric modelling, their limitations and technicaldifficulties are investigated (Shapiro and Vossler 1995).Section 4 of this paper provides details of a pragmaticsolution that produced satisfactory results. Raghothamaand Shapiro (2002) and Hoffmann and Joan-Arinyo (2002)describe additional limitations of parametric modelling butthey are beyond the scope of this paper.

3 Shape optimisation process

Shape optimisation can be viewed as part of structuraloptimisation, a branch of computational mechanics. Themethods for structural optimisation are based on selecting asubset of data to be used as parameters, by means of whichfine-tuning of the structure is performed until the optimalproperties are achieved. Here, the most important aspectis to be able to treat geometry as a variable (Delfour andZolsio 2001).

There are two different ways to implement shape modi-fication within a shape optimisation process. The first oneis closely related to the CAE-centric modelling approach(Section 2), where a geometric modelling system initiallygenerates a computational grid from a model. Next, aselection of points on the grid is perturbed and the modelre-analysed. This process continues until some desired tar-get or termination condition is reached. Examples of this


class of system are MASSOUD (Samareh 2004), Design-Tranair (Melvin et al. 1999), MDOpt (LeDoux et al. 2004)and others (Fenyes et al. 2002). This method is limited bythe allowable displacement of grid points before the gridbecomes inadequate for analysis, inconsistent (e.g., selfcrossing elements), or violates design constraints (e.g., min-imal thickness). The movement of individual points makesshape control difficult to achieve. This type of optimisationis suited for fine tuning of a specific design, but generallyit is not suited for large geometry changes. Despite thesedrawbacks, grid perturbation techniques have proved use-ful in practice, (Carty and Davies 2004; Nemec et al. 2004;Baker et al. 2002; Rhl et al. 1998).

The second type of shape optimisation moves geometrygeneration inside the optimisation loop. It generates a newgeometry model for each point in the design space, thenanalyses the design it represents in each of the different dis-ciplines. This is more closely related to the CAD-centricmodelling approach and it is better suited in situations whenlarge changes in the geometry occur.

We have adopted the second approach, recognising thepotential of the parametric modelling paradigm and the factthat it is supported by modern CAD systems. It offers anelegant way to modify the shape while satisfying predefinedgeometric constraints. Adequately parameterised shape canbe controlled by systems external to CAD using the designtables, where each element of the table corresponds toa value of some variable in the design (line length, arcradius, arc angle etc.). These associations, together withthe appropriate parameterisation, enable us to achieve abovegoals.

The steps in the shape optimisation procedure are pre-sented in Fig. 2. The first step is the construction of a param-eterised CAD model. Parameterisation of a given shape isnot unique, indeed different choices for shape parametersmay be better suited for different aspects of design, anal-ysis and manufacture. For shape optimisation, the modelmust enable automatic generation of a wide range of can-didate shapes, where each shape instance must be feasibleand adhering to the overall design intent. The design intentis encapsulated in the prescribed relationships between thegeometric entities in the model (such as parallelism andtangency) and by the choice and definition of geometricoperations used to construct the shape (such as extrusionor filleting) that give rise to the concept of design features.These aspects, together with the relevant parameter values(lengths, radii etc.) represent the parameterised CAD modelthat is then automatically generated by the CAD system foreach new instance of the parameter vector. As todays sys-tems do not allow different parameterisations of one modelto coexist, the designer needs to make careful choices whendevising the CAD model. When the CAD model is the coreof the product definition, as adopted by the VIVACE project,

Fig. 2 Typical MDO/RD process flow

then the choice of shape control parameters must primarilyadhere to the general principles of Geometric Dimensioning& Tolerancing (GD&T).

The second step in Fig. 2 involves selection of the designmodel, where only subset of the model parameters may beselected for the subsequent optimisation, with the aim toreduce the search space to manageable size.

The third step is a realisation of an automated multidisci-plinary optimisation loop. It involves extracting the neededinformation from the CAD model, modifying the originalparameters and executing the relevant simulation code inorder to evaluate the performance. The optimisation maybe deterministic and/or stochastic. It is important to notethat most of the MDO methods in use today require makinglarge changes in the initial shape in order to better charac-terise the design space and optimise the design according tomultiple criteria.

The fourth step involves robustness assessment of thedesign in relation to the criteria and constraints used in theoptimisation. Monte Carlo simulation may be used for thistask. It is often the case that an optimised design is shownto be too sensitive to small changes in the design parame-ters, i.e. small variations in the shape cause large variation


in performance. This in turn may pose excessive demandson the allowable tolerances, both dimensional and materialproperties, with the consequent implications on the cost oreven feasibility of manufacture.

The final step in the process is the RD optimisation loop.Unlike most MDO methods, RD methods involve smallchanges of the nominal shape, focussing on the assess-ment of the effects of manufacturing tolerances and theuncertainty of material properties (Zhang and Wang 1998).There is also an increasing tendency to combine the twoapproaches into one process, (Giassi et al. 2004).

The implementation details of relevant optimisationloops are largely determined by the choice of design, analy-sis and optimisation tools, often involving in-house analysispackages and bespoke programming using Matlab or lan-guages such as C++. For the work presented in this paperintegration was realised mainly using Matlab in combina-tion with CAD scripts. In addition, commercial optimisationpackages such as iSIGHT/FIPER (www.engineous.com)and modeFrontier (www.esteco.com), increasingly offerfunctionality for integration of different CAD and CAEenvironments. Suitability of these tools for deploymentin a web-based commercial environment was investigatedin other parts of the VIVACE project, (Kesseler and vanHouten 2007).

4 Geometry modelling implementation

As both MDO and RD are executed in a loop, it is crucialto realise shape change without user interaction. Other con-siderations include compatibility with collaborative designpractices, where multiple, geographically dispersed teamstake part in the overall design process. This was efficientlysolved through implementation of a hierarchical modelstructure, where the parametric modelling paradigm allowsall parameters to be stored and modified within designtables. This is depicted in Fig. 3 where each box representsa separate file.

At the top level of the models hierarchy there is anassembly file used as a data collector. In this case it collects

Fig. 3 Model structure

the data defining the solid disc and the blade. Three designtables were constructed to control all the design parameters,specifically:

HPT Disc design tablecontains 48 numerical parame-ters of the 2D section defining the disc.

Firtree Root design tablecontains 20 numerical param-eters of which 10 are associated with the slot on the disc and10 are associated with the corresponding root of the blade.In addition, 11 constants are included in the design table.

Activity design tablecontains the commands to switchon/off the features in the disc master model: rotation, extru-sion cut and circular pattern. Also, it controls the number ofblades by specifying the number of instances for the circularpattern.

An important advantage of the implemented structureis that the shape modifications are introduced at the toplevel only (within the design tables). Thus, parameter val-ues can be modified either interactively, by the user, orautomatically, by a program. The rest of the control struc-ture is updated automatically. The design tables can beimplemented as ASCII text files or as Microsoft Excel files.

4.1 Parameterisation

A geometric definition of the problem must be made beforestarting the optimisation process. The choice of parame-ters is of paramount importance since it is the equivalent todefining the mathematical model of the optimisation prob-lem. Clearly, it defines the nature and the dimensions of theresearch space and possible solutions largely depend on it.

Following the modelling structure outlined above,parameterised disc geometry was implemented and testedon two CAD platforms: CATIA V5 and Unigraphics. Thishighlighted a number of intricate aspects that the designershould consider when defining the model. Figures 4 and 5illustrate the full parameterisation of the HPT rotor. Notethat for the studies presented here, only the root portion ofthe blade needed to be modelled in detail, while the rest ofthe blade was represented by a point mass.

The optimisation algorithm has to be able to find a rela-tionship between the design variable variations and theevolution of performance values. Thus, a controlled mod-ification of the original disc design was required. This wasrealised by implementing scripts that enable the completecalculation process to be entirely performed in batch mode.

An important aspect of parameterisation step is the def-inition of parameter boundaries. At the preliminary designstage these can be used to define a family of parts, whileat the optimisation stage they can define the design spacewithin which the optimisation is performed.

For all CAD packages considered, the likelihood of gen-erating infeasible geometry was found to be highly depen-dent on the choice and size of the parameter subset being


Fig. 4 Parameterized disc

varied, as well as the shape in question and parameteri-sation details. For this reason the permissible parameterboundaries have to be judiciously chosen for each specificoptimisation task. In the case of disc optimisation loopsconsidered here, a subset of eight parameters was varied.

4.2 Model correctness analysis

The constraints prescribed by the model construction resultin a set of simultaneous constraint equations and/or inequal-ities. These equations are solved for the specific instances of

Fig. 5 Parameterised blade rootand slot


Fig. 6 Example of a non-feasible geometry

the parameter values by the constraint solver and the geom-etry of the part is regenerated accordingly within the CADpackage whenever a parameter value is modified (Hoffmanand Joan-Arinyo 1998). As the constraint equations aretypically non-linear, they require the use of iterative meth-ods. With any iterative method, the convergence stronglydepends on the value of the initial guess in relation to thesolution. If the initial guess is far from the correct solution,the method can converge to a wrong solution, as illustratedby the disc geometry in Fig. 6. Such a case is easily identi-fied through the validation readily available within a CADpackage.

On some occasions the method may fail to convergeat all, in which case the software simply returns an errormessage. Bearing this in mind, an important aspect ofthe parameterisation is to ensure, or at least to have highprobability to achieve, the correct shape.

To test the correctness of the design hundreds of sim-ulations involving generation of sets of design parameterswithin the given range were generated in a random fashion.

Table 1 Blade root geometrytest results Range No. of No. of valid

(%) tests geometries

10 100 10020 100 10030 100 10040 100 10041 100 9842 100 9542.5 100 9245 100 9050 100 8260 100 6770 100 34

Table 2 HPT Disc geometrytest results Range No. of No. of valid

(%) tests geometries

10 100 10020 100 10030 100 10031 100 9040 100 7450 100 6060 100 4370 100 27

For each range, 100 random parameter sets were modifiedaround their nominal values using the following formula:

U = U [(1 x) + 2 x Rnd] (1)

where U is a design variable, x is a range and Rnd is arandom number between 0 and 1.

Initially, studies were performed by varying all 48 param-eters of the disc model. This has shown that the permis-sible range of parameter variation is less than 23% ifhigh probability of generating feasible geometry is to beachieved.

Subsequent studies involved varying subsets of eightparameters for the disc and blade root, which were selectedas candidates for optimisation and the results are presentedin Tables 1 and 2. It can be seen that the limit of allowablerange is about 30%. It was also found that smaller jumpsbetween the values are more reliable.

5 Disc design and optimisation

The results of disc optimisation, shown here as an example,were obtained at an early design stage - preliminary shapeoptimisation.

The objective was to find a minimum-weight shape ofthe disc, satisfying given constraints that can be defined interms of maximum stress allowable at a given location, aswell as of burst speed and fatigue life. Only the parametersthat were considered to be most influential in controllingthe overall shape of the disc were optimised, as presented inFig. 7.

An automated, analysis process was set up to perform thenumerical thermo-mechanical calculations. The programwas written in MATLAB and performs following actions:

Launches CATIA and automatically generates the discshape using an ASCII file containing design variablesas input.


Fig. 7 Parameterisation for preliminary disc design

Generates an IGES file needed as the input for the meshgenerator.

Launches the MSC/Patran pre-processor for FE modelset up and automatic meshing

Launches MSC/P-Thermal for the evaluation of thetemperature fields

Launches MSC/Nastran for stress analysis Launches MSC/Robust Design to perform optimisa-

tion and analysis using Stochastic Design improvementmethodology

The communication between different packages is mostconveniently realised through files. Some optimisationloops presented in the subsequent sections involve the use ofdifferent design and analysis tools, but the overall structureis basically the same.

The design parameter values obtained through the opti-misation are presented in Table 3.

The minimum weight shape has been calculated impos-ing that the maximum stress on the disk is smaller than agiven value. Starting from this solution, further features andparameters may be considered in order to further control theshape of the disc and to perform further optimisation on newparameters.

Table 3 Disc optimisationresults Parameter Initial Optimised

p1 70 64p2 10 12p3 80 84p4 655 650p5 54 50p6 120 144p7 370 355p8 430 424

6 Blade root optimisation and robust design

The blade root design must respect three important con-straints:

1. Rupture criteria2. Geometrical relationship criteria3. Stress concentration limits in critical areas

The first constraint dictates that the rupture in the blade(critical stress) must occur before the rupture in the disc.Formally, defining pi as the stress reached in section i and rupture as the ultimate stress of the blade and disc material(Fig. 8), the dimensionless factor Pi is defined as:

Pi = pi/rupture (2)

The following conditions have to be satisfied with theassigned priority:

P1 > P2 (mandatory condition)P1 > P4 (mandatory condition)P2 > P4 (desirable condition)

The second constraint, geometrical relationship criteria,concerns the relative feature sizes of the blade root and thedisc. Defining md the smallest sectional area in the disc slotand mp the smallest sectional area in the blade root (seeFig. 8), the following condition has to be satisfied:

Kl 0MPS YTS < 0pr_1 KyYTS < 0pr_2 KyYTS < 0

Geometric parameters (the solution of the preceding optimi-sation) were perturbed with the normally distributed noisecharacterised with standard deviation of 3%. In order toreduce the required number of simulations without sacrific-ing the quality of the statistical description of the systembehaviour, descriptive sampling was used to generate apopulation of 500 samples (Saliby 1990).

Table 5 provides the results of the robustness assess-ment expressed as a sigma-level. It can be seen that whilethe optimised solution achieves a high sigma-level regard-ing maximal principal stress and contact pressures, thesigma-level for the constraint P1P2 is unacceptably low at0.6.

6.3 Optimising for six sigma

To improve the robustness of the blade root design, prob-abilistic design optimisation formulation, as presentedby Koch et al. (2004), was implemented. It combinesapproaches from structural reliability and robust design withthe concepts and philosophy of Six Sigma. Variability isincorporated within all the elements of this probabilisticformulationinput design variable bound formulation, out-put constraint formulation and robust objective formulation.

The implementation involved an automatic optimisationloop, in which Monte Carlo simulations are performedwithin each iteration. The overall objective was to determinea blade root design according to the stated criteria, whileachieving six-sigma level of design robustness in relation tothe prescribed output constraints.


Fig. 10 Distribution ofsectional tensions a before andb after blade root optimisation

The blade root six-sigma based probabilistic design opti-misation formulation is given as follows:

Find the set of design variables X that minimises:

MPS, MPSpr_1, pr_1pr_2, pr_2

Subject to:

P1 6P1 > P2 + 6P2MPS + 6MPS YT S < 0pr_1 + 6pr_1 YTS < 0pr_2 + 6pr_2 YTS < 0

The minimisation function has thus been expanded to

include minimisation of both the mean and the standarddeviation of stress. Also, the output constraints have beenreformulated so that the mean plus six standard deviationsis within the constraints bounds for all the outputs.

This approach was implemented within modeFrontier de-sign environment and the optimisation was carried out againusing a multi-objective genetic algorithm. At each step, 50

Table 5 Blade root analysis: performance quality results derived fromthe Monte-Carlo analysis

Mean StDev Sigma level

MPS_1YTS 389 11.4 > 10MPS_2YTS 474 4.89 > 10pr_10.6YTS 282 5.58 > 10pr_20.6YTS 244 8.42 > 10P1 P2 5.5E3 8.3E3 0.66

Monte Carlo simulations were conducted and the responsemean and standard deviation were computed. The over-all process involved 1,000 optimisation steps and the totalcomputing time was about 5 days.

It has been suggested (Marczyk 2000) that one way toimprove the overall computational time would be to use themethod of stochastic multidisciplinary improvement. In thisapproach, a set of N random samples is generated aroundthe nominal design. A target location in the performancespace is defined and the Euclidean distance of each sampleto the target is computed. The best one is chosen as a start-ing point for the next step of N points. This approach hasmany aspects in common with the presented robust designapproach and it is the subject of our future research.

The results from the Six Sigma based probabilistic opti-misation is shown in Table 6 in which the new mean andstandard deviation values of the output performances arereported. It can be noted that a high sigma level wasachieved for all constraints, including the constraint P1 P2for which it was previously unacceptably low. At the sametime these results may be considered to be overly conserva-tive because all sigma levels are >10. However, the mainpurpose of the presented exercise was to demonstrate the

Table 6 Blade root analysis: performance after the six-sigma basedprobabilistic optimisation

Mean StDev Sigma level

MPS_1YTS 449 7.81 > 10MPS_2YTS 467 3.08 > 10pr_10.6YTS 243 4.45 > 10pr_20.6YTS 246 5.68 > 10P1 P2 6.6E3 4.8E4 > 10


overall performance capability and in practice such resultswould be assessed in the wider context of the specificationof the engine as a whole. For example, although con-servative, this design may still comply with the overallweight specifications and the expense of further optimisa-tion may not be necessary. Otherwise the minimisation canbe modified to include additional constraints.

7 Conclusions

The work presented in this paper was conducted as anattempt to realise Robust Design and Multi DisciplinaryOptimisation methodologies in the context of the require-ments posed by the aerospace industry, where the overallobjectives involve continual reduction of development costsand lead times, while improving the product performanceand reliability. In view of the complexity of the product andthe need to integrate efforts by teams specialising in variousinterdependent disciplines, CAD was adopted as the princi-pal repository for product data definition and the principalsource of data for various design optimisation processes.

Design optimisation methods require CAD tools to beinvoked in an automated loop, in spite of such tools beingintended primarily for interactive use. The issues related tovariational modelling using parametric CAD models, oftenleading to generation of incorrect or infeasible geometry,are well documented in the literature. As the permissiblerange of parameter variation is in practice difficult to pre-dict, the solution was found to be two-fold. First, only asubset of the geometric parameters was selected for optimi-sation, leading to significantly larger range of permissiblevariation than when using all parameters in the model. Thechoice of parameters necessitates detailed knowledge of theproblem in hand and judgement by experienced designers,Second, for the chosen set of optimisation parameters, thepermissible variation ranges can be adequately estimatedusing Monte Carlo simulation. As a result, the ability toperform structural optimisations involving both small andlarge changes in part shape was demonstrated with highprobability of producing feasible and satisfactory solutions.

The methodology was implemented and applied in thespecific case of gas turbine high pressure disc design. Theprescribed design procedure and complexity were consid-ered to be representative for this class of engineering prod-uct. The results demonstrated the validity of the overallapproach, while the final design was shown to meet relevantdesign requirements and to achieve significant performanceimprovements.

Acknowledgments The work presented is part of the EU framework6 VIVACE project. The authors acknowledge the collaboration fromour industrial partners Avio, Rolls-Royce and MTU.

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CAD based shape optimization for gas turbine component designAbstractIntroductionGeometric modelling for shape optimisationShape optimisation processGeometry modelling implementationParameterisationModel correctness analysis

Disc design and optimisationBlade root optimisation and robust designOptimisationRobustness assessmentOptimising for six sigma

ConclusionsReferences

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CAD Based Shape Optimization for Gas Turbine Component Design