Free-Free, Fixed or Other Test Boundary Conditions for the Best Modal Test?

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1 Free-Free, Fixed or Other Test Boundary Conditions for the Best Modal Test? S. Perinpanayagam and D. J. Ewins Vibration Engineering Centre Mechanical Engineering Department Imperial College of Science, Technology and Medicine Exhibition Road London SW7 2BX Tel: Fax: ABSTRACT Deciding on the configuration in which to test a structure is an important consideration which needs to be addressed before a test is carried out. Since the evolution of the modal test, there are several test configurations - free-free, fixed, added-mass, amongst others- that have been developed and used. However, the free-free test configuration remains the most favoured for most applications since it is easy to achieve this configuration in practice. In this paper, different test configurations are compared and their benefits and limitations for the respective applications are discussed. It is also shown by using a simple study that information obtained from a free-free test is not adequate to validate mathematical s for certain applications. In these cases alternative test configurations are suggested and their ability to provide modal information for validation are discussed. 1. INTRODUCTION Since the evaluation of the modal test, several test configurations, including free-free, fixed and mass-added configurations, have been used in various applications to characterise the structure's dynamic behaviour. Free-free configurations are commonly used in modal testing since it is easy to achieve this type of configuration in practice. In a free-free test configuration, the structure is supported from a suspension system designed so as to ensure that the rigid body's mode frequencies are at least an order of magnitude lower than the fundamental frequency of the structure. It is very difficult to provide truly flexible suspension systems for testing of large flexible space structures under zero gravity. In these cases fixed-base boundary configurations are preferred. They are also called constraint boundary configurations. Fixedbase or constraint-boundary modal tests have traditionally been used to verify and improve the dynamic of a constraint structure since the measured modes and frequencies can be used directly in verification processes. However, there are number of difficulties associated with fixed-base modal testing. These difficulties can, in some cases, make the approach impractical. First it is impossible to achieve a truly fixed-base test since the fixture will have some degree of coupling with the test article. The extent of contamination of the test data due to such coupling depends on the number of fixture modes and the characteristics of these modes, within the frequency bandwidth of the test. Secondly undesired motion may occur the test article and the fixture connection that are welded, bolted or constructed using lubricated bearings. Finally the cost of designing and constructing a fixture for a fixed-base modal test may be prohibitive. To provide alternative approaches when fixed-base testing proves impractical, mass additive testing was developed. Coleman and Anderson [5] and Admire, et al. [1] used mass additive testing for simple boundary simulation to approximate an in-situ configuration for a space shuttle flight pay-load. Traditionally, a fixed-based modal test has been performed as a means of verifying the coupled loaded mathematical. Mass additive testing is cost effective in that an expensive test fixture with unknown boundary conditions is replaced by a relatively inexpensive, reusable and known boundary condition which does not contaminate the modal test results with fixture-coupled modes or boundary condition uncertainties. Gwinn, et al. [7] and Baker [3] consider the use of the mass-additive method for component mode synthesis.

2 Perturbed Boundary Condition (PBC) is a derivative of mass additive testing. In PBC testing simple mass addition or stiffness modifications are used to perturb the structure for the purpose of getting additional information about the structure's behaviour from the changes in the structure's modal parameters. It was first used for verification and correction of dynamic s of structures in the early 1990s [6]. One of the historical problems associated with finite element (FE) validation (verification and correction) has been in measuring enough information to localise the errors in the. Generally the test data captured during a modal test are modally and spatially truncated, and sometimes heavily so. Insufficient modal and spatial information in the test data can lead to a situation whereby analytical s with good correlation to the test data can be produced. However, they cannot predict the effect of modification on the structure or changes to the boundaries. Li et al. demonstrate how by using PBC testing, more useful test data can be obtained from the modal test for validation [8], [4], [9]. In this paper, different test configurations are compared and their benefits and limitations are discussed with respect to validation. 2. VALIDATING ANALYTICAL STRUCTURAL MODELS USING MODAL TESTS The development of analytical s for structural systems is one of the basic requirements for structural analysis. It is widely accepted that these s ought to be experimentally validated before they are accepted as the basis for final design analysis. Recent efforts to address this problem have resulted in the development and evaluation of algorithmic methods for structural correlation and refinement. However, there are still questions relating to what test configurations, freefree, fixed, mass-added or others, the structure needs to be tested in to obtain informative test data about the structure to validate the. This issue is even more important when the structure is complicated and consists of many components and sub-assemblies. In this instance using modal tests to validate the analytical of the assembly may be difficult due to noise and several other mechanisms such as non-linear behaviour of joints. Generally it is very difficult to get any sensible information beyond the first few rigid and flexural modes. With little information from the test, it is very difficult to employ validation processes to correct many structural parameters in the assembly which are incorrect in the. Performing vibration modal tests of smaller sub-assemblies and individual components remain an effective way of overcoming these disadvantages. However, in reality the individual components of an assembly are constraints in the assembly configuration and when performing the modal test on them individually, it is important that their boundary conditions are carefully chosen such that important dynamic parameters can be obtained from the test for validating their mathematical s. Currently in most cases the validation test is performed in a free-free configuration since it is easy to achieve this boundary condition in reality. However, it will be shown using a case study that the modal parameters obtained using a freefree configuration provide very little information about some of the important spatial parameters, e.g. joint stiffness, that need to be validated for assembly analytical s. Since this research is aimed at identifying boundary conditions for validating aircraft engine casing components for engine assembly, an assembly of five cylindrical casing components are used in the following case study. 3. VALIDATING CYLINDRICAL CASING STRUCTURE A cylindrical casing assembly, as shown in Figure 1, was used for the case study for discussing the different boundary conditions. This assembly consists of five components of similar profile as shown in Figure 2. The two dimensional profile of the component is also shown in Figure 2. Figure 1: A Cylindrical Casing Assembly This profile was chosen since it has a simple cylindrical profile in the middle except at positions where the casing is attached to the next casing. Also it is very similar to casing structures used in aircraft engines. The aspect ratio of diameter to length of the casing is chosen similar to the engine casing structures.

3 Figure 2: Component Profile Two s of the component structure were created. The first one is a detailed solid and the second one is a simplified shell and beam. They are shown in Figure 3. Figure 3: Solid Model (Test Data) and Shell Model (Analytical Model) The solid of the component was created using the CHEXA solid element in Nastran and the was created using CQUAD4 shell elements for the body and CBAR beam elements for the flanges in Nastran. For this case study, instead of using test data from the casing structure, analysis modal data from the solid was used. The shell and beam was considered as the analytical of the casing structure. Furthermore, since the is an analytical, some of the spatial parameters, particularly the geometrical properties (Ixx and Iyy) of the flange were deliberately assigned incorrect values such that the had to be corrected and validated with the test data (solid ). As discussed before, in the new test strategy, to obtain a valid for the cylindrical casing assembly, validation has to be performed at the component level. In the following sections, different test configurations are compared and their respective abilities to provide information about the component for validating it for assembly dynamic behaviour are discussed. Before discussing the different boundary conditions for components, the solid s modal parameters (test data) and the 's modal parameters (analytical ) are compared. 3.1 Comparison of analytical of the cylindrical casing assembly with the test data In Table 1 of Appendix 1, the correlated mode pairs and their frequencies (from the solid ) for the cylindrical casing assembly are given. Table 1 of Appendix 1 also shows the frequency difference in percentage points the analytical and the test data ( vs. solid ). It can be seen that the modes which have significant effect by erroneous spatial parameters at the flange are the first bending mode of the assembly. The frequencies of the two nodal diameter two nodal ring (2ND-2NR) and two nodal diameter three nodal ring (2ND-3NR) also show high deviations. The bending mode and the 2ND-2NR modes are shown in Figure 4. Figure 4: The bending mode and the 2ND-2NR mode The frequencies are considered to be significantly deviated when the frequency difference the analytical and test data is greater than 5% From the above analysis we can conclude that the bending modes are very sensitive to erroneous spatial parameters in the flange. Most of the diameteral modes are not sensitive at all to the erroneous parameters at the flanges (joint stiffness).

4 3.2 Comparison of the modal parameters from the component and test data for free-free configuration With the concept of the new test strategy, the modal parameters are compared at the component level for the free-free configuration. Table 2 of Appendix 1 shows the test frequency and frequency difference the real structure and the analytical for correlated mode pairs. The highest frequency deviation obtained for the correlated mode pairs is less than three percentage points of the real structure. Hence it can be deduced that the first twenty-five diameteral modes of the freefree configuration do not have a significant effect due to the erroneous spatial parameters at the flanges of the analytical. Also if we used the free-free configuration to perform a validation, we can obtain a perfectly validated analytical for the cylindrical casing s components. However, when this is used in the assembly, it will predict the bending modal parameters incorrectly. Some of the higher modes (around 5000Hz) of the free-free configuration show frequency deviations greater than 5%. However in reality these modes are difficult to instrument and measure since they are complex, localised modes of the flanges. 3.3 Comparison of the modal parameters from the component and test data for fixed configuration Table 3 of Appendix 1 shows the test frequency and frequency difference the real structure and the analytical for correlated mode pairs. In this configuration the frequency difference of the two nodal diameteral modes shows the highest deviation of sixteen percent. Also the first bending mode and the three nodal diameteral mode show deviations of twelve percent and five percent respectively. Considering the free-free configuration, the fixed configuration is very sensitive to the erroneous spatial parameters at the flanges of the analytical. Hence more informative modal parameters can be obtained to validate the analytical. One important observation from the fixed configuration is that the higher diameteral modes (forth, fifth and sixth) have very little frequency deviation and hence are less sensitive to the erroneous spatial parameters at the flanges of the analytical. Even though this configuration is ideal to validate component s of the cylindrical casing for assembly configuration, in reality it is very difficult to achieve a truly fixed-base test since the fixture will have some degree of coupling with the test article. 3.4 Comparison of the modal parameters from the component and test data with alternative boundary condition Disc Figure 5: Casing component with 70mm disc A seventy millimetre rigid disc was attached to the component as an alternative boundary condition as shown in Figure 5. Table 4 of Appendix 1 shows the test frequency and frequency difference the real structure and the analytical for correlated mode pairs. Similar to the fixed configuration, the bending and two nodal diameteral modes show very high deviation when the analytical was compared to the test data. Hence, this configuration is in many ways similar to the fixed configuration discussed in Section 3.3. It is also very informative, when compared to the free-free configuration, in providing some important modal parameters to validate the component for assembly configuration. Another important observation, similar to the fixed configuration, is that the higher nodal diameteral modes (forth, fifth and sixth) have very little frequency deviation and hence are less sensitive to the erroneous spatial parameters at the flanges of the analytical. Furthermore, apart form mode five and six in which the disc vibrates with the casing structure, the disc acts as very rigid structure in all the other modes. Unlike the fixed configuration which is very difficult to achieve, this disc is very easy to manufacture and to attach to the casing. Hence it is an ideal configuration to test the casing s components to validate their s for assembly configuration. 4. CONCLUSION The free-free configuration is commonly used in modal testing to obtain test data for validation since it is easy to achieve this configuration in practice. However, from the above case study, this configuration is not adequate to provide informative test data to validate mathematical s for certain applications. This statement is particularly true when modal tests are performed on components to validate the component s s for assembly behaviour. In this instance, the free-free configuration contains very little information, in a limited frequency range of measurement, related to the joints of an assembly to validate them at component level. In these cases performing a modal test with alternative boundary conditions is considered. These alternative boundary conditions can be chosen such that very informative test data can be obtained from the modal test for validation. They can be designed such that they are easily manufactured and attachable to the component structure.

5 ACKNOWLEDGEMENTS The authors wish to thank the Commission of the European Union for financial support provided for the CERES (Cost-Effective Rotordynamic Engineering Solution) project. REFERENCES 1. Admire, J. R., Tinker, M. L., and Ivey, E. W., "Mass Additive Test Method for Verification of Constrained Structural Models", AIAA Journal 31 (11), pp , Admire, J. R., Tinker, M. L., and Ivey, E. W., "Residual Flexibility Test Method for Verification of Constrained Structural Models", AIAA Journal 32 (1), pp , Baker, M., "Component Mode Synthesis Methods for Test-Based, Rigidly Connected, Flexible Components", AIAA , Proceedings of the 25 th Structures, Structural Dynamics and Materials Conference, pp , May Barney, P., Pierre, M. S., and Brown, D. L., "Identification of a Modal Model Utilizing a Perturbed Boundary Condition Test Method", Proceedings of the 10 th International Modal Analysis Conference, Coleman, A. D., Anderson, J. B., Driskill, T. C., and Brown, D. L., "A Mass Additive Technique for Modal Testing as Applied to the Space Shuttle ASTRO-1 Payload", Proceedings of the 6 th International Modal Analysis Conference, pp , February Chen, K. N., Nicolas, V. T., and Brown, D. L., Perturbed Boundary Condition Model Updating, Proceedings of the 11th International Modal Analysis Conference, Gwinn, K. W., Lauffer, J. P., and Miller, A. K., "Component Mode Synthesis Using Experimental Modes Enhanced by Mass Loading", Proceedings of the 6 th International Modal Analysis Conference, pp , February Li, S., Shelley, S. and Brown, D. L., "Perturbed Boundary Condition Testing Concepts", Proceedings of the 13 th International Modal Analysis Conference, Yang, M. and Brown, D. L., "Model Updating Techniques Using Perturbed Boundary Condition (PBC) Testing Data", Proceedings of the 14 th International Modal Analysis Conference, 1996.

6 APPENDIX 1 Mode ND in ND in ND anti ND anti ND 2NR ND 2NR st Bending st Bending ND 3NR ND 3NR ND anti ND anti ND in ND in ND 2NR ND 2NR ND 3NR ND 3NR Table 1: Comparison of analytical with the test data for the cylindrical casing assembly Mode ND in ND in ND anti ND anti ND in ND in ND anti ND anti ND in ND in ND in ND in ND anti ND anti ND in ND in ND anti ND anti ND anti in ND anti in ND anti in ND anti in ND anti ND anti ND in Table 2: Comparison of component s analytical with the test data for free-free configuration

7 Mode ND ND ND ND ND ND ST Bending ST Bending ND ND ND-2NR ND-2NR ND-2NR ND-2NR ND ND ND-2NR ND-2NR Torsional ND-2NR ND-2NR ND-2NR ND-2NR ND ND Table 3: Comparison of component s analytical with the test data for fixed configuration Mode ND ND ND ND ND anti ND anti ND ND Bending Bending ND ND ND-2NR ND-2NR ND-2NR ND-2NR ND ND ND-2NR ND-2NR Torsion ND-2NR ND-2NR Table 4: Comparison of component s analytical with the test data with an alternative boundary condition