Title:

Kind
Code:

A1

Abstract:

A method of optimising a design of a component is described. The method comprises the steps of: representing a base design as a CAD model comprising a plurality of geometric entities, assigning a tag name to each geometric entity, transferring the design into an analysis code and determining an optimum design from the analysis code.

The tag names associate boundary conditions to the geometric entities such as temperature, velocity or mesh density if the analysis code is a Finite Element Analysis code.

Inventors:

Armstrong, Ian (Bristol, GB)

Rees, Janet (Gloucestershire, GB)

Song, Wenbin (Southampton, GB)

Rees, Janet (Gloucestershire, GB)

Song, Wenbin (Southampton, GB)

Application Number:

10/407196

Publication Date:

10/30/2003

Filing Date:

04/07/2003

Export Citation:

Assignee:

ROLLS-ROYCE plc. (London, GB)

Primary Class:

International Classes:

View Patent Images:

Related US Applications:

Primary Examiner:

DAY, HERNG DER

Attorney, Agent or Firm:

OLIFF PLC (ALEXANDRIA, VA, US)

Claims:

1. A method of optimising a design of a component by conducting analyses on a set of design variants, each analysis comprising the steps of: (a) representing the design variant as a CAD model comprising a plurality of geometric entities, (b) assigning a tag name to each geometric entity, (c) creating a computerised analysis model from the CAD model wherein the tag names remain associated with the respective geometric entities, (d) assigning boundary conditions to at least one of the geometric entities in the analysis model by reference to the tag name, and (e) determining an output condition of the analysis model in response to the boundary conditions, the method further comprising the step of selecting an optimum variant on the basis of the results of the analyses.

2. A method of optimising a design of a component as claimed in claim 1, wherein the determination of an output condition comprises determining an output condition of at least one of the geometric entities in the analysis model by reference to the tag name of that entity.

3. A method of optimising a design of a component as claimed in claim 1, wherein the set of design variants is generated by use of a computer algorithm.

4. A method of optimising a design of a component as claimed in claim 3, the geometric entities comprising at least one dimension, wherein the set of design variants is generated by modifying a dimension of at least one of the geometric entities.

5. A method of optimising a design of a component as claimed in claim 3, wherein the set of design variants is generated by the addition or removal of at least one geometric entity.

6. A method of optimising a design of a component as claimed in claim 1, wherein the generation of the set of design variants includes generating a design variant by modifying a previous design variant in response to the output condition of the previous design variant.

7. A method of optimising a design of a component as claimed in claim 5, wherein the association between each tag name and corresponding geometric entity is unaffected by the removal or addition of a geometric entity.

8. A method of optimising a design of a component as claimed in claim 1, wherein a mesh density is associated with at least one of the geometric entities by reference to the tag name of that entity.

9. A method of optimising a design of a component as claimed in claim 1, wherein the analysis model is a thermo-mechanical finite element analysis model.

10. A method of optimising a design of a component as claimed in claim 1, wherein the analysis model is a computational fluid dynamics model.

11. A method of optimising a design of a component as claimed in claim 1, the geometric entities having at least one model property applied to it, wherein at least one of said model properties of at least one of the geometric entities is associated with the tag name of that geometric entity.

12. A method of optimising a design of a component as claimed in claim 11, wherein the model property is a material property of said geometric entity.

13. A method of optimising a design of a component as claimed in claim 11, wherein the model property is a temperature of said geometric entity.

14. A method of optimising a design of a component as claimed in claim 1, which is performed as a batch process, the design variants being generated automatically as the process proceeds until an optimum design variant is achieved.

15. A method of manufacturing a component, the method comprising: (a) optimising the design of the component by a method in accordance with claim 1; (b) manufacturing the component in accordance with the optimised design.

16. A method of manufacturing a component as claimed in claim 15, in which the component is a component of a gas turbine engine.

17. A method as claimed in claim 16, in which the component is a turbine blade having a fir tree root, the design of at least the fir tree root being optimised by a method in accordance with claim 1.

18. A component having a design optimised by conducting analyses on a set of design variants, each analysis comprising the steps of: (a) representing the design variant as a CAD model comprising a plurality of geometric entities, (b) assigning a tag name to each geometric entity, (c) creating a computerised analysis model from the CAD model wherein the tag names remain associated with the respective geometric entities, (d) assigning boundary conditions to at least one of the geometric entities in the analysis model by reference to the tag name, and (e) determining an output condition of the analysis model in response to the boundary conditions; and selecting an optimum variant on the basis of the results of the analyses.

19. A component manufactured by optimising the design of the component by conducting analyses on a set of design variants, each analysis comprising the steps of: (a) representing the design variant as a CAD model comprising a plurality of geometric entities, (b) assigning a tag name to each geometric entity, (c) creating a computerised analysis model from the CAD model wherein the tag names remain associated with the respective geometric entities, (d) assigning boundary conditions to at least one of the geometric entities in the analysis model by reference to the tag name, and (e) determining an output condition of the analysis model in response to the boundary conditions; selecting an optimum variant on the basis of the results of the analyses, and manufacturing the component in accordance with the optimised design.

20. A computer program product comprising code for carrying out a method of optimising a design of a component by conducting analyses on a set of design variants, each analysis comprising the steps of: (a) representing the design variant as a CAD model comprising a plurality of geometric entities, (b) assigning a tag name to each geometric entity, (c) creating a computerised analysis model from the CAD model wherein the tag names remain associated with the respective geometric entities, (d) assigning boundary conditions to at least one of the geometric entities in the analysis model by reference to the tag name, and (e) determining an output condition of the analysis model in response to the boundary conditions, the method further comprising the step of selecting an optimum variant on the basis of the results of the analyses.

21. A computer system adapted to carry out a method of optimising a design of a component by conducting analyses on a set of design variants, each analysis comprising the steps of: (a) representing the design variant as a CAD model comprising a plurality of geometric entities, (b) assigning a tag name to each geometric entity, (c) creating a computerised analysis model from the CAD model wherein the tag names remain associated with the respective geometric entities, (d) assigning boundary conditions to at least one of the geometric entities in the analysis model by reference to the tag name, and (e) determining an output condition of the analysis model in response to the boundary conditions, the method further comprising the step of selecting an optimum variant on the basis of the results of the analyses.

2. A method of optimising a design of a component as claimed in claim 1, wherein the determination of an output condition comprises determining an output condition of at least one of the geometric entities in the analysis model by reference to the tag name of that entity.

3. A method of optimising a design of a component as claimed in claim 1, wherein the set of design variants is generated by use of a computer algorithm.

4. A method of optimising a design of a component as claimed in claim 3, the geometric entities comprising at least one dimension, wherein the set of design variants is generated by modifying a dimension of at least one of the geometric entities.

5. A method of optimising a design of a component as claimed in claim 3, wherein the set of design variants is generated by the addition or removal of at least one geometric entity.

6. A method of optimising a design of a component as claimed in claim 1, wherein the generation of the set of design variants includes generating a design variant by modifying a previous design variant in response to the output condition of the previous design variant.

7. A method of optimising a design of a component as claimed in claim 5, wherein the association between each tag name and corresponding geometric entity is unaffected by the removal or addition of a geometric entity.

8. A method of optimising a design of a component as claimed in claim 1, wherein a mesh density is associated with at least one of the geometric entities by reference to the tag name of that entity.

9. A method of optimising a design of a component as claimed in claim 1, wherein the analysis model is a thermo-mechanical finite element analysis model.

10. A method of optimising a design of a component as claimed in claim 1, wherein the analysis model is a computational fluid dynamics model.

11. A method of optimising a design of a component as claimed in claim 1, the geometric entities having at least one model property applied to it, wherein at least one of said model properties of at least one of the geometric entities is associated with the tag name of that geometric entity.

12. A method of optimising a design of a component as claimed in claim 11, wherein the model property is a material property of said geometric entity.

13. A method of optimising a design of a component as claimed in claim 11, wherein the model property is a temperature of said geometric entity.

14. A method of optimising a design of a component as claimed in claim 1, which is performed as a batch process, the design variants being generated automatically as the process proceeds until an optimum design variant is achieved.

15. A method of manufacturing a component, the method comprising: (a) optimising the design of the component by a method in accordance with claim 1; (b) manufacturing the component in accordance with the optimised design.

16. A method of manufacturing a component as claimed in claim 15, in which the component is a component of a gas turbine engine.

17. A method as claimed in claim 16, in which the component is a turbine blade having a fir tree root, the design of at least the fir tree root being optimised by a method in accordance with claim 1.

18. A component having a design optimised by conducting analyses on a set of design variants, each analysis comprising the steps of: (a) representing the design variant as a CAD model comprising a plurality of geometric entities, (b) assigning a tag name to each geometric entity, (c) creating a computerised analysis model from the CAD model wherein the tag names remain associated with the respective geometric entities, (d) assigning boundary conditions to at least one of the geometric entities in the analysis model by reference to the tag name, and (e) determining an output condition of the analysis model in response to the boundary conditions; and selecting an optimum variant on the basis of the results of the analyses.

19. A component manufactured by optimising the design of the component by conducting analyses on a set of design variants, each analysis comprising the steps of: (a) representing the design variant as a CAD model comprising a plurality of geometric entities, (b) assigning a tag name to each geometric entity, (c) creating a computerised analysis model from the CAD model wherein the tag names remain associated with the respective geometric entities, (d) assigning boundary conditions to at least one of the geometric entities in the analysis model by reference to the tag name, and (e) determining an output condition of the analysis model in response to the boundary conditions; selecting an optimum variant on the basis of the results of the analyses, and manufacturing the component in accordance with the optimised design.

20. A computer program product comprising code for carrying out a method of optimising a design of a component by conducting analyses on a set of design variants, each analysis comprising the steps of: (a) representing the design variant as a CAD model comprising a plurality of geometric entities, (b) assigning a tag name to each geometric entity, (c) creating a computerised analysis model from the CAD model wherein the tag names remain associated with the respective geometric entities, (d) assigning boundary conditions to at least one of the geometric entities in the analysis model by reference to the tag name, and (e) determining an output condition of the analysis model in response to the boundary conditions, the method further comprising the step of selecting an optimum variant on the basis of the results of the analyses.

21. A computer system adapted to carry out a method of optimising a design of a component by conducting analyses on a set of design variants, each analysis comprising the steps of: (a) representing the design variant as a CAD model comprising a plurality of geometric entities, (b) assigning a tag name to each geometric entity, (c) creating a computerised analysis model from the CAD model wherein the tag names remain associated with the respective geometric entities, (d) assigning boundary conditions to at least one of the geometric entities in the analysis model by reference to the tag name, and (e) determining an output condition of the analysis model in response to the boundary conditions, the method further comprising the step of selecting an optimum variant on the basis of the results of the analyses.

Description:

[0001] This invention relates to a method of optimising the design of a component. More specifically, although not exclusively, the invention relates to the automation and optimisation of the design of a component using a computer aided design (CAD) system and a computer aided analysis system and a method of transferring data between the two.

[0002] It is well known to use CAD systems when designing a component. It is also common practice to use the CAD model as a basis for models to be analysed by computer to determine the suitability and limits of the design. Such analysis models may be, for example, a computational fluid dynamics model or a thermo-mechanical finite element analysis model. A single CAD representation of the geometry forms the basis of each analysis model. The use of parametric CAD has enabled this geometry to be automatically updated when the value of the dimension of a design entity, for example a fillet radius, is changed. In a parametric CAD tool design variables may be associated with these dimensions to enable the component geometry to be varied, creating a new design variant. For a given set of parameters a particular instance of the geometry may be generated for export to an analysis code. Geometry is typically transferred to the analysis code using a neutral data standard file format, eg IGES, Step, or a custom written interface which provides a link between a specific CAD and analysis package.

[0003] In order to automate this process successfully the geometry model and the analysis model need to be linked such that any change to the geometry is automatically reflected in the analysis model. This process must maintain the associativity between the geometry and the analysis model definition, eg boundary conditions and domain properties. The ability to extract results based on the new geometry needs to be provided to enable the design criteria to be automatically evaluated.

[0004] Known techniques are based on the assumption that the CAD package will export the entities in a consistent order during the translation process. Each geometric entity is assigned an entity number during the translation process, which is used within the analysis code to identify the geometry. This identification number is used to assign boundary conditions and extract results.

[0005] This process breaks down where topology changes occur, for example the addition and deletion of entities, or where the ordering changes. In such cases, the entity number assigned to a geometric entity during translation may not be the same as in a previous iteration. The process, therefore, is not robust where significant shape changes are required.

[0006] For example, one iteration of a design during an optimisation process may have a central hole which is absent in a subsequent iteration. The loads, mesh densities and other domain properties and boundary conditions are stored in sequence alongside the geometric entities of the component. If one of these geometric entities, such as the hole, is removed, the listing of the domain properties and boundary conditions may lose their correct associations with the geometric entities, and the system would fail.

[0007] According to a first aspect of the present invention there is provided a method of optimising a design of a component by conducting analyses on a set of design variants, each analysis comprising the steps of:

[0008] (a) representing the design variant as a CAD model comprising a plurality of geometric entities,

[0009] (b) assigning a tag name to each geometric entity,

[0010] (c) creating a computerised analysis model from the CAD model wherein the tag names remain associated with the respective geometric entities,

[0011] (d) assigning boundary conditions to at least one of the geometric entities in the analysis model by reference to the tag name, and

[0012] (e) determining an output condition of the analysis model in response to the boundary conditions,

[0013] the method further comprising the step of selecting an optimum variant on the basis of the results of the analyses.

[0014] The method may further comprise the step of determining an output condition of at least one of the geometric entities in the analysis model by reference to the tag name. The set of design variants may be generated using a computer algorithm, and this step may be achieved by modifying a dimension of at least one of the plurality of geometric entities, or by adding and/or removing at least one geometric entity.

[0015] The tag name may associate a mesh density with the geometric entity to which it is assigned.

[0016] The computerised analysis model may be a finite element analysis model or a computational fluid dynamics model.

[0017] A model property of at least one of the geometric entities is preferably associated with the tag name of that geometric entity. This model property may be a material property, a temperature or a speed of the geometric entity.

[0018] According to a second aspect of the present invention there is provided a component having a design optimised by conducting analyses on a set of design variants, each analysis comprising the steps of:

[0019] (a) representing the design variant as a CAD model comprising a plurality of geometric entities,

[0020] (b) assigning a tag name to each geometric entity,

[0021] (c) creating a computerised analysis model from the CAD model wherein the tag names remain associated with the respective geometric entities,

[0022] (d) assigning boundary conditions to at least one of the geometric entities in the analysis model by reference to the tag name, and

[0023] (e) determining an output condition of the analysis model in response to the boundary conditions; and

[0024] selecting an optimum variant on the basis of the results of the analyses.

[0025] According to a third aspect of the present invention, there is provided a component manufactured by optimising the design of the component, by conducting analyses on a set of design variants, each analysis comprising the steps of:

[0026] (a) representing the design variant as a CAD model comprising a plurality of geometric entities,

[0027] (b) assigning a tag name to each geometric entity,

[0028] (c) creating a computerised analysis model from the CAD model wherein the tag names remain associated with the respective geometric entities,

[0029] (d) assigning boundary conditions to at least one of the geometric entities in the analysis model by reference to the tag name, and

[0030] (e) determining an output condition of the analysis model in response to the boundary conditions;

[0031] selecting an optimum variant on the basis of the results of the analyses, and manufacturing the component in accordance with the optimised design.

[0032] The component may be a component of a gas turbine engine, and may be a turbine blade having a fir tree root.

[0033] According to a forth aspect of the present invention there is provided a computer program product comprising code for carrying out a method of optimising a design of a component by conducting analyses on a set of design variants, each analysis comprising the steps of:

[0034] (a) representing the design variant as a CAD model comprising a plurality of geometric entities,

[0035] (b) assigning a tag name to each geometric entity,

[0036] (c) creating a computerised analysis model from the CAD model wherein the tag names remain associated with the respective geometric entities,

[0037] (d) assigning boundary conditions to at least one of the geometric entities in the analysis model by reference to the tag name, and

[0038] (e) determining an output condition of the analysis model in response to the boundary conditions,

[0039] the method further comprising the step of selecting an optimum variant on the basis of the results of the analyses.

[0040] According to a fifth aspect of the present invention, there is provided a computer system adapted to carry out a method of optimising a design of a component by conducting analyses on a set of design variants, each analysis comprising the steps of:

[0041] (a) representing the design variant as a CAD model comprising a plurality of geometric entities,

[0042] (b) assigning a tag name to each geometric entity,

[0043] (c) creating a computerised analysis model from the CAD model wherein the tag names remain associated with the respective geometric entities,

[0044] (d) assigning boundary conditions to at least one of the geometric entities in the analysis model by reference to the tag name, and

[0045] (e) determining an output condition of the analysis model in response to the boundary conditions,

[0046] the method further comprising the step of selecting an optimum variant on the basis of the results of the analyses.

[0047] This invention thus provides a novel step within the design automation loop, in which a unique text string in the form of a tag name is assigned to each geometric entity within the CAD tool. This tag name is then used within the analysis code to define the associativity between the analysis model properties (boundary conditions, result locations) and the geometry.

[0048] A component geometry is described in a CAD system by a number of geometric features, eg lines, arcs, NURBS etc whose relationship and dimension are prescribed by the designer. In a parametric CAD tool design variables may be associated with these dimensions to enable the component geometry to be varied. For a given set of these parameters a particular instance of the geometry may be generated for export to an analysis code. This export may utilise a neutral data standard, eg IGES or STEP or a custom written translator, written to link a particular CAD and Analysis package. A number of CAD tools have the ability to assign a unique text string, or tag name, to each geometric entity, eg line, surface, volume. In this invention the analysis code utilises this information to generate the associativity between the geometry and the analysis model properties.

[0049] The analysis code provides the ability to define all the properties of the model by tag name. These include boundary conditions, mesh densities, and domain boundaries and properties (a domain is a user-defined region of a model; the region is represented by a set of surfaces in 2D or a set of volumes in 3D.) Examples of domain properties include speeds, temperatures, material properties and thicknesses (2D models only).

[0050] The model can then be automatically regenerated based on this definition and the new geometry (plus tag names) output from the parametric CAD model. The analysis code also provides the capability to extract the results required, using these tag names to identify the region of interest, for example, peak stress over an entity (line, surface or volume) or average stress along a section constituting the minimum section length between two entities in the form of edges. Introducing this facility enables a robust link to be generated between the parametric CAD model and the analysis model, without the restriction imposed by a constant topology. This enables the design/analysis loop to be run in batch, which is a requirement for geometric shape optimisation.

[0051] For a better understanding of the present invention and to show how it may be carried into effect, reference will now be made by way of example to the accompanying drawings, in which:—

[0052]

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[0074]

[0075] The overall architecture of the design optimisation process is illustrated in

[0076] With reference to

[0077] As a first step in a design process with the objective of optimising the design of the component

[0078] Data relating to the geometry and the associated tag names is then exported to the preferred analysis code. This is done either by transferring the data in a neutral format, or via a translator used to convert the CAD data into a format recognised by the analysis software.

[0079] The analysis model defined by the analysis code is then used to simulate the behaviour of the component. This is done by applying boundary conditions and domain data to the model. As shown in

[0080] If the CAD system used does not provide the capability to export tagged data, a new facility in the analysis code which automatically tags the geometry on import may be used. These tags would then be used throughout the analysis for each corresponding entity. The tags would be used as a reference when, for example, the mesh density or a model property such as temperature is applied to the geometric entities.

[0081] The use of tag names creates the possibility of automating the results extraction during analysis. A new facility in the analysis code enables the user to define the output results locations using the tag names. For example, the system could be asked to extract the peak worst principal stress which occurs on the entity “RESULTSEDGE”.

[0082] As an example, if the user wished to modify the hole radius to Z and output the new peak stress on the edge

[0083] (1) open the CAD tool

[0084] (2) open the analysis tool

[0085] (3) run the analysis and extract the peak stress on the tagged entity “RESULTSEDGE”.

[0086] This process may be controlled via a batch script without user intervention. This enables the whole process to be linked to an optimiser to identify the best set of design variable values to meet a set of design limits, for example to achieve minimum component mass while meeting the requirement that the peak stress at the edge

[0087] As a detailed example, an optimisation process incorporating the present invention will now be described with reference to the optimisation of a fir tree root component as used in the turbine engines to attach a blade to a turbine disk.

[0088] Here, the design of the fir-tree geometry is carried out using ICAD. The basic procedure of the geometry design falls into two steps: first identification of the features and rules used to define the geometry and secondly the breaking down of the whole model into several modules, each of which becomes a building block in a hierarchical structure. In ICAD, each of these basic blocks is described using the ICAD design language (IDL) as a generic definition which can be implemented in the ICAD browser using a specific set of parameter values. Thus the model is defined parametrically: different sets of parameter values will result in different designs from the same template. In addition, multi-modality and backward compatibility can be achieved by incorporating different behaviours into one model with a single interface while only the internal implementation is modified.

[0089] A single basic tooth geometry

[0090] The acceptability of any fir-tree geometry needs to be checked since some particular combination of parameters may result in unacceptable features such as intersections between entities or the collapse of very short entities. The handling of unacceptable features is important to the optimisation process as well as to the analysis code. Using ICAD, geometry features can be checked within the modelling process, as part of the whole model and appropriate actions can then be taken using preset default values, while signalling which parameter is causing the problem. Taking the modelling of the base tooth

[0091] Here, the blade root

[0092] The first fir-tree geometry

[0093] Every entity within the ICAD model can have additional non-geometric properties which will ease the use of the geometry in other applications such as analysis and manufacture. This object-oriented feature enables various information related to a product design to be integrated into a single model. For example, to apply boundary conditions and loads to entities during the analysis stage, it is desirable to name the entities with unique tag names which can then be referenced later. Using tag names on each entity in the geometry enables the boundary conditions, load properties and mesh parameters to be specified in batch mode.

[0094] Geometric quantities such as the minimum thickness of the blade root, the distance between the centre of the contact face of the tooth on each side, etc, are calculated in the ICAD model based on a mathematical representation of the geometry. Some of these are treated as constraints in the optimisation problem and some are used to retrieve analysis results. For example, point coordinates are normally required to get the stress values at those points. Alternatively, if a tagged geometric entity is specified the worst principal stress at that entity may be found.

[0095] 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 action of the gas pressure on the airfoil and forces due to tilting of the airfoil. The resulting stress distribution in the root attachment area is a function of geometry, material and loading conditions (which are of course related to the speed of rotation). It is known that some critical geometry features exist for the stress distribution in the blade disk interface.

[0096] Many studies into the stress state of the blade root attachment have been reported, originally using photo-elastic methods, now mainly using finite element analysis. Modern finite element codes already have the capability of dealing with thermal-mechanical coupling and contact analysis between blade root and disk head. It is now relatively easy to obtain the stress distribution in the attachment area using commercial FE codes. Also many in-house FE codes exist to handle corporate-specific problems (these have some advantages over commercial tools among which the most notable is complete control over the source code). Although there are many kinds of code available, the general procedure of finite element analysis is almost always as follows:

[0097] (1) Create the geometry, or import the geometry from another CAD system;

[0098] (2) Apply the boundary conditions and loads;

[0099] (3) Mesh the geometry;

[0100] (4) Solve the problem and retrieve the results.

[0101] Most FE codes support batch running of the analysis and this allows the analysis to be embedded into the overall optimisation loop. Smooth coupling of the modelling process and analysis, however, is not an easy task. It involves the transfer of the geometry itself and related geometry dependent properties to the analysis code, in this case, the finite element software

[0102] The loading on the root is mainly due to centrifugal load which is dependent on the mass of the whole blade. The design of the fir-tree root involves an iterative process of controlling the blade mass, which incorporates the root mass. Also some key features, such as the fillet radius, play very important roles in the stress distribution in notch regions. Thus a set of competitive constraints ranging from geometrical, mechanical, cooling requirements, etc, is established for use in exploration of various design candidates for the fir-tree root. Finite element analysis is then utilized to obtain the resulting stress distributions. This further complicates the situation. A traditional manual method is now too slow for this process and thus automation is required. Four types of constraints are used to check the design:

[0103] Crushing stress describes the direct tensile stress on the teeth: bedding width is the main factor affecting the stress.

[0104] Unzipping can occur after a blade release: the disk post on either side of the released blade are then subject to high tensile and bending stresses. The disk post must be able to withstand these stresses in order to avoid a progressive ‘unzipping and release’ of all the blades

[0105] Disk neck creep: the disk posts are subject to direct tensile stress which causes material creep. Too much creep, combined with low cycle fatigue, can dramatically reduce the component life.

[0106] Peak stresses: peak stresses occur at the inner fillet radii of both the blade and the disk. If the fillet radii are too small and produce unacceptable peak stresses, some bedding width has to be sacrificed to make them bigger.

[0107] Apart from the above constraints, which are used to check the candidate designs, some others are used to check the optimised result. These include vibration limits, neck stress, etc From a preliminary blade number optimisation, these criteria are not deemed a significant constraint here.

[0108] As the fir-tree geometry is constant along the root centre line, it is possible to think of the stresses as two dimensional. However, the loading applied along the root centre line is not uniform, so strictly speaking, the distribution of stresses will be three dimensional. Nonetheless, it is still possible to assume that each section behaves essentially as a two dimensional problem with different loadings applied to it. The difference of loading on each section is affected by the existence of skew angle which will increase the peak stresses in the obtuse corners of the blade root and the acute corners of the disk head. From previous root analysis research, it is feasible and convenient to use a factor to estimate the peak stresses at each notch of the blade and disk, and this factor takes different values for different teeth.

[0109] Also, it is known from previous work using photo-elastic and finite element methods, that the distribution of centrifugal load between the teeth is very non-uniform and the top tooth may take a significant portion of the load. This feature allows the possibility of using different tooth sizes. The system implemented here also allows designers to explore the effect of varying the number of teeth, but this may cause difficulties when gradient-based methods are used for optimisation.

[0110] Both a one sector model and a three sector model are considered when estimating the mechanical constraints, the one sector model for the estimation of maximum notch point stresses, crushing stresses and blade/disk neck mean stresses and the three sector model for the estimation of unzipping stresses. Typical FE results are illustrated in

[0111] It will be appreciated that the condition shown in

[0112] The whole process from the importing of geometry, application of boundary conditions and loading, to results retrieval is implemented here as a SC03 Piugin, which is a facility provided by the Rolls-Royce in-house FEA code SC03 to extend the capability of its core functionality. A command file is used by SC03 to carry out jobs ranging from importing geometry from IGES files, applying boundary conditions and loads, to retrieving stress results.

[0113] Two different optimisation problems were tackled using population based genetic algorithms (GAs) and gradient-based methods. One was to minimize the area outside of the last continuous radius of the turbine disk, 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 dependent on the number of teeth. The other was to find the optimum tooth profile to minimize the maximum notch stress. The design variables (see

[0114] The constraints are divided into two categories, geometric and mechanical, which are summarized in

[0115] a. constraints with upper bounds only:

[0116] b. constraints with lower bounds only:

[0117] c. constraints with both upper and lower bounds:

[0118] These different formula make it possible for all normalized constraints to have consistent behaviour when the design is moving from an infeasible region towards feasibility, and to have the values of −1 or +1 at the boundary of the constraints.

[0119] It is necessary to establish the appropriate values for mesh control parameters. The purpose is to find a compromise between the high computational costs that are incurred for very fine meshes and the accuracy required to capture the maximum stresses in the notch area. Therefore, the local and global effects of mesh density must be studied.

[0120] Following the set up of the system, a series of systematic evaluations is carried out to establish appropriate mesh density parameter values and to gain experience on the effects of design variables changes. From varying the mesh density control parameters while holding all others constant, for example the global and local edge node spacing, it is found that reducing the notch edge node spacing increases the mesh density and therefore reduces the perturbations in maximum notch stress. In this example the use of 0.001 mm for both global and local edge node spacing has been chosen as a suitable value. The effect of different geometric features on the stress distribution within the structure are summarized in

[0121] From parameter study results it can be seen that the notch stress on the second tooth takes the largest value, as already implied from previous work: this aspect makes it desirable to design each tooth using different values of tooth profile parameters.

[0122] With reference to

[0123] In the process illustrated in

[0124] Owing to the presence of a discrete design variable (the number of teeth), most gradient based optimisation techniques will not work directly here. Therefore a two-stage strategy of combining a Genetic Algorithm (GA) with gradient search may be used in this problem. A typical GA is first employed in an attempt to give a fairly even coverage on the search space, and then gradient based search methods are applied on promising individuals with the number of teeth fixed. One of the considerations here is that generic algorithms are capable of dealing with discrete design variables. Another consideration is that as the GA proceeds, the population tends to saturate with designs close to all the likely optima including sub-optimal and globally optimum designs, while gradient based methods are more suited to locating the exact position of individual optimum given suitable starting points. Here the GA is used to give good starting points for the gradient search methods.

[0125] In this example an initial analysis on the base design reveals that several geometric and mechanical constraints are violated. These include geometric constraints

[0126] Genetic algorithms often require large number of evaluations of the objective function and constraints. The computational cost involved can soon become prohibitively high when computationally intensive finite element analysis is used to calculate the stresses in the structure. In this problem each evaluation takes about 5-6 minutes to finish, and most of this time is engaged in finite element analysis. This means that it takes about 80 hours to finish a 10 generation GA search with a population size of 100 using serial processing. (Note that for some specific sets of parameters, there is no viable geometry that can be constructed, and when this occurs SC03 is simply signalled to cancel the analysis).

[0127] Because of the large number of design variables, the optimisation trace may only be plotted on contour maps of two variables if these maps are produced while holding all the other variables constant. Furthermore, if only a small number of quantities are chosen as design variables, there may be no feasible designs at all. For an infeasible starting design, it is easier for the optimiser to find a feasible region if a large number of quantities are left as design variables and broad exploratory searches are used.

[0128] A contour map for two design variables has been generated using results from the GA search (

[0129] A gradient based search is illustrated in

[0130] Several steepest descent search methods have been applied to the problem after the initial GA search: these include the Hooke and Jeeves direct search method plus various other methods discussed in Schwefel's book. The first method is very fast when the number of design variables is small, as shown in

[0131] A 20% reduction in the objective function is achieved in this example using the above methods while satisfying all the geometric and mechanic constraints. By looking at the trace data of the search process, it can be seen that the three geometric constraints and the disk notch stresses (identified earlier) remain the major factors affecting the optimisation results. Note that the primary changes to geometry occurred during the GA search and are as illustrated in

[0132] Although minimising the frontal area, and thus the rim-load will reduce overall weight, the life of blade/disk is highly dependent on the notch stresses, and so the notch stress may be minimised to achieve required life targets. Therefore, following the search on the full scale problem, a second optimisation problem to minimize the maximum notch stress has been carried out, starting from the best design found in the previous search. It is expected that this search will drive the geometry in a different direction given the changed goal. The result is shown in

[0133] 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 cost evaluation or manufacturing requirements could be further included without sacrificing the compatibility of the existing model. A complete and consistent product model could then be achieved to be set up for evaluation in the design optimisation process.