SUPERMODEL VALIDATION FOR STRUCTURAL DYNAMIC ANALYSIS OF AERO-ENGINE COMPONENTS

Transcription

1 SUPERMODEL VALIDATION FOR STRUCTURAL DYNAMIC ANALYSIS OF AERO-ENGINE COMPONENTS C. Zang, C. Schwingshackl, D. J. Ewins Centre of Vibration Engineering, Department of Mechanical Engineering, Imperial College London, Exhibition Road, London, SW7 2AZ, UK NOMENCLATURE { φx } The reference mode shapes { A } φ The mode shapes of a FE prediction MAC(A,X) Modal Assurance Criterion H Complex conjugate transpose ABSTRACT This paper discusses validation for aero-engine components using supermodel. A supermodel is a very detailed solid finite element model. It is usually created with a much finer mesh and can be considered to be capable of reliably representing all geometric features such as holes, flanges, fillets of the actual structure, and its dynamic properties, i.e. the natural frequencies and mode shapes. Therefore, information provided from a supermodel can be treated as a trusted source of reference which, to some extent, closely represents the experimental data measured on a component and can be employed in virtual experiments, where the boundary conditions can easily be controlled to simulate the response behaviour. It would obviously be advantageous to help to construct and update the design model in the early stage of design process in order to massively reduce the design process cycles if such an approach was itself proven to be effective. However, the concept of 'supermodel' requires itself to be validated before it can be used in the validation of aero-engine models in the design process in the aeronautics industry. This paper explores the feasibility of creating supermodels for aero-engine components and the reliability of replacing test data by the information from supermodels in model validation. An intermediate casing, which is a complex component in a whole engine model, and a Combustor Outer Casing (COC) are used as examples to demonstrate that dynamic properties of supermodels are capable of closely representing those of the actual structures. Criteria and guidelines for the creation of 'supermodels' that have the capability of producing reliable reference data to replace practical testing of prototypes of aero-engine components are also discussed. 1. INTRODUCTION One of challenges on the whole engine development in the competitive aero-engine industry intends to massively reduce the burden of maintaining an up-to-date whole engine model as the design requires more detail and fidelity [1]. One of critical issues is to accelerate the model validation process for efficient design verification of major components. A traditional validation procedure relies on experimental tests on the actual structure. However, in most practical cases, it is cost and time consuming for constructing prototypes for a new design or a modified design, on which the experiments can be undertaken. It is usually too late in the design/modification loop to make the validated design model available. Therefore, it is important to find a proper approach to increase the ability to adapt an engine model quickly in the design process. A supermodel is a very detailed solid finite element model that, subject to the level of physics permitted in the model, can match the test data from a physical structure with excellent accuracy [2]. A supermodel can be considered to be capable of representing all geometric features such as holes, flanges, fillets of the actual structure, and its dynamic properties, i.e. the natural frequencies and mode shapes, can be taken as

2 representative of those of the actual structure. As a supermodel can provide much more detailed information in both the frequency and spatial domains than can be provided by experimental measurement, and can be ideally employed in virtual experiments, where the boundary conditions can easily be controlled to simulate the response behaviour, it would obviously be advantageous to help to construct and update the design model in order to massively reduce the design process cycle. For example, if reference data generated from a supermodel can be used to replace the reference test data from a physical test structure, then the model updating of the design model will be performed using two FE models (a supermodel and a design model). This approach removes the need to build a physical test structure, and to plan and perform a modal test from the validation process in the direct design cycle loop. Therefore, the large labour cost and the elapsed time are significantly reduced. However, the concept of 'supermodel' requires to be validated itself before it can be used in the validation of aero-engine models in the design process in the aeronautics industry. This paper will focus on supermodel validation for aero-engine casing components. Section 2 will introduce the model validation process of aero-engine components, and Section 3 will discuss their supermodel validation. It includes exploring the feasibility of creating supermodels for aero-engine components and the reliability of replacing test data by the information from supermodels in model validation. An intermediate casing, which is a complex component in a whole engine model, and a Combustor Outer Casing (COC) are used as examples to demonstrate that dynamic properties of supermodels are capable of closely representing those of the actual structures. The criteria or guidelines for the creation of 'supermodels' that have the capability of producing reliable reference data to replace practical testing of prototypes of aero-engine components are also discussed. 2. MODEL VALIDATION OF AERO-ENGINE COMPONENTS Conventionally, validation of an FE model of an aero-engine component for structural dynamics analysis needs a set of reference data, usually provided as a set of modal properties or FRFs. The process of model validation is described in Figure 1. Figure 1 Flow chart of conventional model validation process A conventional model validation process relies on experimental reference data of the structural dynamic properties of the prototype. It requires that an actual structure or prototype is available to conduct the tests and its reliability depends on the accuracy and completeness of the experiments. Building a structure (or constructing a prototype) and carrying out modal tests occupies a significant amount of the design cycle time so that the validated design model normally becomes available too late in the design/modification loop. This approach is also costly as it requires the manufacture of special prototypes and experimental tests. A further

3 problem originates from the limited information obtained by modal tests in both the frequency and spatial domains. The amount of information gained from testing is normally too small to modify all the parameters of the FE model. In this case, only some of the parameters can be selected for modification during the model updating process and the differences between the structural dynamics properties of the prototype and those of the model predictions can only be minimized to some extent. As the concept of 'supermodel' is now increasingly accepted in the aero-engine industry, design models of aeroengine components can be validated using virtual 'experimental' data obtained from computing simulation (virtual methods). Instead of test results in the conventional model validation, the reference data used here for the correlation and updating of the design model is gained from predictions made using a supermodel. Therefore, the correlation and updating of the design model will be performed using two FE models (a supermodel and a design model). Figure 2 shows the flow chart of the model validation process by virtual methods. Figure 2: Flow chart of the model validation process by virtual methods The advantage of model validation by virtual methods is that the virtual 'experimental' data provide more than enough information for the process of model correlation and updating. Moreover, the drawback of measurement incompleteness, encountered in conventional model validation, can be overcome and, thus, the ill-conditioning problems and non-uniqueness in model updating may be mostly avoided. From a supermodel, more eigenvalues can be produced and more accurate eigenvectors can be represented at as many DOFs as required. This more detailed reference response resource can be exploited to assess the level of accuracy of the design model and to evaluate whether it is itself fit for use. 3. SUPERMODEL VALIDATION FOR AERO-ENGINE COMPONENTS As the supermodel is finely meshed to represent detailed geometrical features of the aero-engine component with great accuracy, information provided from a supermodel can be treated as a trusted source of reference which, to some extent, closely represents the experimental data tested on a component. It can be used in the early stage in the aero-engine development programme for validation of the design model, which is usually coarse meshed. However, explorations of the feasibility of creating supermodels for aero-engine components and the reliability of replacing test data by the information from supermodels in model validation are required before the concept of 'supermodel' is applied to the validation of aero-engine models in the design process in the aeronautics industry. The criteria or guidelines for the creation of 'supermodels' that have the capability of

4 producing reliable reference data to replace practical testing of prototypes of aero-engine components are also required to be developed. 3.1 Feasibility of creating supermodels for aero-engine components A refined and detailed FE model needs to be verified before it can be used as a 'supermodel' to represent closely the structural dynamic properties. One of the major procedures of model verification is to check the convergence of the model. The convergence-predicted modes from a supermodel should cover the number of modes (or the frequency range) investigated in the design process Finite Element Models of IMC One example of an FE model verification is demonstrated using an Intermediate casing (IMC), a complex aeroengine structural component. The IMC geometry was supplied by Volvo Aero Corporation and several detailed FE models were created by INBIS. The model is an asymmetric component and consists of ten struts joining the hub to the outer casing. Figure 3 shows the geometry and an FE model of IMC. A comprehensive investigation of the FE models built with various mesh densities and provided comparative data on meshing times, quality of elements, mass discrepancies, etc. was discussed in [3] and a brief summary is introduced here for convenience. IMC Geometry IMC Solid Model Figure 3 IMC geometry and a FE solid model To assess the suitability of the finite element model, six meshes of the complete model with Tet10 elements have been produced; each with different global element edge lengths. The DOFs of each of the meshed IMC models with varying global element edge lengths (GEEL) lists below in Table 1. Obviously, the DOFs of the model increases significantly when the control parameter of the global element edge length is reduced. It indicates how much more computing resources will be required to solve larger models. Table 1 The dofs of the meshed IMC models (1M=1000,000) GEEL(mm) No. of Dofs 4.5M 4.6M 5M 5.6M 6.8M 11M Verification of IMC Finite Element Models To check the convergence of various meshed IMC models, a normal mode vibration analysis was performed using an MSC.Nastran SOL103 solver. Natural frequencies for first 34 modes are considered, excluding the first 6 rigid body modes. A comparison of these natural frequencies for the various meshes is plotted in Figure 4. It can be seen that all natural frequencies computed from the 6 meshed models are generally in good agreement, especially for the first 19 modes which are highly matched among these six models. From mode 20 to mode 34, a noticeable difference can be seen in the model with 10mm global element edge length, compared to the other 5 models with finer meshes which are grouped more closely. This may be due to the discrepancy errors between fine and finer meshes. The model with 10mm global element edge length has the largest variation in mass among the all meshed models.

5 The deviation in natural frequencies compared to the 4.5mm global element edge length model is shown in Table 2. More clearly, the finer the mesh is, the better the convergence will be, although all models were convergent to some extent. It also indicates that the modes in the higher frequency range are more sensitive to the discrepancy errors in the model. Therefore, a 'fit-for-purpose' model can be created if a finer mesh is performed. However, when a structure becomes large and complex, a detailed model will demand significant computational resources. It is necessary to develop a robust technique to create a 'fit-for-purpose' supermodel to meet the target. In this example, if our frequency range of interest is between the first 34 modes and our interest is overall structural stiffness, it can be seen that models meshed with 4.5mm, 6mm, 7mm and 8mm global element edge lengths respectively are considered to be fit for the purpose and can be treated as 'supermodels' Frequency (Hz) mm 6.0mm 7.0mm 8.0mm 9.0mm 10.0mm Mode No. Figure 4 Natural frequencies for various meshed models of IMC 3.2 Reliability of creating supermodels of aero-engine components for simulation of test data The modelling study of an intermediate casing, which is a complex component in a whole engine model, shows the feasibility of creating 'fit-for-purpose' supermodels if refined and detailed meshes are produced. 'Verified' supermodels are those models that are convergent within the interested frequency range. However, it does not mean that these models are validated models. Actually, it only means that these models are ready to be subjected to a model updating procedure for validation and could possibly become validated models. Even though the models are validated later, these validated models are limited to these convergent-predicted modes within the interested frequency range. In order to determine if a supermodel can be used as the reference data to replace the experimental test, one or more sets of experimental data have to be used as the reference to verify or update the supermodels. Another aero-engine component, Combustor Outer Casing (COC), is used here to illustrate the validation of supermodels and to demonstrate the reliability of creating supermodels of aero-engine components for replacement of test data Study case of supermodel validation via test data: COC component Three detailed FE models of a COC component were created from the COC geometry model for the purpose of supermodel validation. TET10 solid elements were used in various meshes on each of the models. A modal test on a real structure was carried out and experimental data (natural frequencies and mode shapes on 60 measured DOFs) were obtained from modal analysis by LMS [4]. The test model that is simply a mesh that joins together the test measurement points for ease of visualisation and post processing, three supermodels, and the real structure are shown in Figure 5. Details of three FE models (supermodels), namely SM1, SM2, and SM3, are listed in Table 3.

6 Table 3 Three solid models of the COC Name Nodes Elements DOFs SM1 ( Model1) M SM2 (Model 2) M SM3 (Model 3) M A) Test Model B) The real structure C) Model 1(SM1): Refined solid model D) Model 2 (SM2): More refined model E) Model 3 (SM3): The most Refined model Figure 5 The COC real structure, test model and three FE models The convergence of three supermodels (SM1, SM2, and SM3) was checked by the comparison of natural frequencies obtained from the MSC.Nastran SOL103 normal modes vibration analysis. The frequency range we are interested in is between 1~500Hz. Therefore, natural frequencies up to 16 modes for SM1, SM2, and SM3 are considered exclusive of the first 6 rigid body modes. Results show that natural frequencies of the first 16 modes are in good agreement and all three models are convergent. The validation process of the three supermodels was undertaken using the ICATS tools developed at Imperial College. Nastran analysis results of these three models were transferred into.dsp and.eig files for correlation analysis using Patran neutral file which includes the geometry of the model and patran report including mode shapes information. The geometry and mode shapes of the test model were saved as LMS universal files. Before the correlation analysis, the two models were associated into the same local coordinate system and then the model matching step was taken in order that nodes on both models are perfectly matched. Finally, the matched nodes are employed for correlation analysis Comparison of frequencies

7 The first comparison to make is of the measured versus the predicted natural frequencies from FE models. Figure 6 shows the experimental values plotted against the predicted ones for each of the modes included in the comparison in order to see the degree of correlation between the two sets of results and any possible discrepancies which exist. As can be seen, all natural frequencies lie close to a straight line, indicating that no erroneous material properties have been used in the predictions. Another comparison is based on natural frequency difference (NFD) between the TM and the predicted SMs (SM1, SM2, and SM3). NFDs are usually calculated from the established correlated mode pairs (CMPs) during the process of model correlation. Table 4 lists the NFDs between the experimental and the FE predicted data sets from SM1, SM2, and SM3. All the NFD parameters between the TM and the SMs (SM1, SM2, SM3) are within 3% excluding the CMP modes 11, 12, 15, and 16, which are between 4.27% ~ 5.70%, respectively in the cases of the TM vs. the SM2 and the TM vs. the SM3. a) The TM vs. the SM1 b) The TM vs. the SM2 Figure 6 Comparisons of natural frequencies between the TM and the SMs Table 4 Natural frequency difference (NFD) between the TM and the predicted SMs (%) Name TM vs SM1 TM vs SM2 TM vs SM3 Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Comparison of mode shapes The comparisons between measured and predicted mode shapes were quantified by the MAC (Modal Assurance Criterion) parameters. The MAC is defined by [5],

8 2 H H H { } { } { } { } { } { } MAC( A, X ) = φ φ φ φ φ φ X A X X A A where subscripts X and A refer to reference (test) and the FE predictions, respectively. Clearly, The MAC is a scalar quantity, and is a useful mean of quantifying the comparison between two sets of mode shape data, even if the mode shape data are complex. A MAC value is a real scalar from zero to unity. A Mac value of 1 represents a total agreement of the compared mode shapes while a value of 0 indicates a total disagreement. The MAC can also be normalized by a weighting matrix that is provided either by the mass or stiffness matrices of the system. One of the more practical approaches uses the SEREP-based reduction process (System Equivalent Reduction Expansion Process). In this approach, a pseudo-mass matrix computed using either the limited measured eigenvectors, or the preferred corresponding analytical ones, is used as a weighting matrix. This correlation coefficient has an advantage over the MAC in that it is more sensitive to the actual similarity or dissimilarity between the mode shapes. The normalized MAC sometimes referred as the SEREP-Cross- Orthogonality (SCO) correlation coefficient will generally have a higher value for two similar mode shapes than the MAC correlation coefficient and, conversely, a lower value for two dissimilar mode shapes. Firstly, the AutoMACs, in which a set of mode shape vectors are correlated with themselves, are calculated and all the diagonal values in the MAC matrixes (TM vs SM1, TM vs. SM2) are close to unity and the off-diagonals are zero. Therefore, all modes are orthogonal. Secondly, the MAC matrixes between the experimental mode shapes and analytical eigenvectors predicted from the supermodels (SM1, SM2) are shown in Figure 7. It can be seen here that all the experimental modes are correlated with both analytical modes. Looking carefully at the diagonal values of MAC tables, we can see the MAC values for modes 1 to 4, 11, and 12 in both pictures are between 60-80%. To improve the MAC values in correlation, the normalised cross orthogonality (SCO) correlation, namely, SCOMAC, is used and results are plotted in Figure 8 and the diagonal MAC values are listed in Table 5 a) MAC table of the TM vs. SM1 b) MAC table of the TM vs. SM2 Figure 7 MAC tables of the TM vs the SMs

9 a) SCOMAC table of the TM vs the SM1 b) SCOMAC table of the TM vs the SM2 Figure 8 SCOMAC tables of the TM vs the SMs Table 5 MAC and SCOMAC values of TM vs SMs Name TM vs SM1 TM vs SM2 MAC (%) SCOMAC (%) MAC (%) SCOMAC (%) Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode As expected, the correlation values have greatly improved, although they are unlikely visible in Figures 7 and 8. Another correlation between two supermodels (SM1 vs. SM2) is also carried out and MAC values are plotted in Figure 9. A perfect correlation obtained.

10 Figure 9 MAC tables of the SM1 vs the SM Further discussion It is noted that the supermodel SM3 is not involved in the validation process due to the extra large size of the model. As the model has 6.8M DOFs, the Nastran input file is as large as 300Mb and the.xdb output file produced for the analytical results takes the size of about 3 Gb. For ICATS tools, correlation analysis needs a.dsp and an.eig files transferred from Patran neutral and Patran report files. Unfortunately, Patran failed to read the large Nastran input file due to limited default memory setup for the reading Nastran input module. After setting up a large memory size for the program, the Nastran input model was finally loaded into Patran, but Patran crashed again when outputting the geometry of the model. Alternatively, we visualized and compared the mode shapes and natural frequencies between the SM3 and other two supermodels (SM1, SM2) as well as the test model. We are confident that SM3 is also a valid supermodel. 3.3 Guidelines for creation of supermodels for aero-engine components Model Investigations of the feasibility and the reliability of creating supermodels for aero-engine components have demonstrated that dynamic properties of supermodels are capable of closely representing those of the actual structures. Therefore, the supermodel approach can be offered to provide the reference behaviour by virtual simulation instead of experimental test on actual structures. As there are no test data to validate supermodels during the preliminary design stage, it is especially important for both model developers and users to understand the limitations of these models and to ensure that supermodels are created and used correctly. The following guidelines based on Patran mesh software tools will be helpful for creation of 'fit-for-purpose' supermodels for aero-engine components [6]. Supermodels are generally created with fine meshes using solid elements in order to represent the geometric details of the structure as closely as possible. Models can be meshed automatically and directly from CAD geometry. To verify the quality of supermodel creations, checks on following issues are required; Element type: Tetrahedral elements are simply used for automatic meshing. Based on practical experience, the TET4 should be avoided for implicit structural analysis because TET4's are linear (first order) elements and often bring problems related to 'numerical locking'. Furthermore, TET4' are much stiffer than TE10's and therefore will not give realistic results. Therefore, it is suggested that TET10 should be used instead of TET4. TET10's are quadratic (second order) elements and need particular control on thin curved sections. For a complex structure, a very large of TET10's are required. Element shape checks: It is required to perform element distortion checks in order to measure quantities of modelling. The general checks include aspect ratio, edge angle and face skew, collapse ratio, etc. More details can be found in [4].

11 Mass check: The mass checks are a useful means of verifying that the proper mass of the structure was retained throughout the reduction process in the modelling. Mesh connectivity between segments: As the meshing program copes better with the smaller, less complicated solid geometry, it may be required to break the model into segments for large complex structures in order to improve the mesh quality on all meshes. When connecting all segments, mesh match at boundary of adjoining solids is required. Patran has the function to deal with it using the 'assembly parameters/match parasolid faces' within the 'Finite element/create mesh' facility. Once completed, standard checks are required to ensure correct mesh connectivity at the boundaries. After verifying the quality of a supermodel, further analytical checks are needed to characterise the dynamics of the structure. The major step is to check the convergence of the model. The convergedpredicted vibration modes from the supermodel should cover the number of modes or the frequency range required in the preliminary design process. The control parameter of the global element edge length determines the numbers of nodes, elements, and DOFs of a supermodel. The smaller the value of the global element edge length is selected, the finer meshed model can be produced, but the size of model will be significantly increased. Therefore, further solution of the model and interrogation of the results files demands more computer resources. The 'fit-forpurpose' supermodel needs to balance the size of model and the computing resources by choosing an appropriate value of the GEEL parameter. The supermodel meshed from the CAD geometry is not the same as the model created from the manufactured structure due to the manufacturing tolerances. When the supermodel is too refined, the discrepancy between the dynamic properties predicted from the supermodel and those from the actual structure will be affected because of the contributions of uncertainties of FE modelling in geometry and in the material properties. Therefore, a supermodel needs to have some robustness and be insensitive to the manufacturing uncertainty parameters. 4. CONCLUDING REMARKS The feasibility of creating supermodels for aero-engine components and their reliability for representation of test data are demonstrated using aero-engine structural components. Results shows that supermodel can be treated as a trusted source of reference to represent closely the experimental test data and can be employed in virtual methods. Besides, guidelines for creation of fit-for-purpose supermodels for aero-engine components are also discussed. ACKNOWLEDGMENTS The financial support of the European Commission under the Sixth Framework Programme Priority 4 Aeronautics and Space through VIVACE project (Contract No ) is gratefully acknowledged. The authors also wish to thank Rolls-Royce plc, INBIS, AOLVO Aero Corporation, and LMS International for providing FE models of aero-engine components and modal test data on the structure. REFERENCES [1] European project VIVACE (Value Improvement through a Virtual Aeronautical Collaborative Enterprise) Framework VI. Description of Work version 3.0 Part 3. Jan [2] C. Zang, G. Chen and D. J. Ewins. Task Model validation and updating: report on competitive assessment of updating methods. A technical deliverable for EC Framework 6 Integrated Project VIVACE, ref: VIVACE 2.3/3/IMP/T/ , December, p1-49 [3] Philip Baker, Finite element meshing of the 'use-case' intermediate casing model in support of the creation of 'fit-for-purpose' supermodels'. A technical deliverable for EC Framework 6 Integrated Project VIVACE, ref: VIVACE 2.3/3/INBIS/T/ , April, 2006 [4] Daniele Ghiglione, Bart Peeters, and Antonio Vecchio 'Early test interpretation methods'. A technical deliverable for EC Framework 6 Integrated Project VIVACE, ref: VIVACE 2.3/2/LMS/T/06220, June, 2006

12 [5] D. J. Ewins 'Modal Testing Theory, practice and application', Second Edition, Research Studies Press LTD. Baldock, Herthfordshire, England, 2000 [6] C. Zang, C. Schwingshackl and D. J. Ewins. Task Model validation and updating: report on methods and tools for supermodel validation and design model verification via supermodels. A technical deliverable for EC Framework 6 Integrated Project VIVACE, ref: VIVACE 2.3/3/IMP/T/ , August, p1-62

13 Table 2 The deviation in natural frequencies compared to the 4.5mm GEEL model Mode No. 4.5 vs vs vs vs vs