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IMPACT OF TEST DATA UNCERTAINTIES ON MODAL MODELS EXTRACTED FROM MULTI-PATCH VIBRATIONS TEST.

Antonio VECCHIO1, Lorenzo VALENT2, Luigi BREGANT2 1 2

LMS International, Interleuvenlaan 68, B-3001 Leuven, BELGIUM

Dipartimento di Ingegneria Meccanica - Università di Trieste, 10 Via Valerio - 34127 Trieste, ITALY

SUMMARY This paper presents the results of an experimental campaign aimed at assessing the impact of vibration data uncertainties on the quality of modal models extracted from test data. Focus is given to data uncertainties induced by mass loading effect in multi-patch modal tests. Several different patterns for sensor distribution over the test article are taken into account, modal models as extracted form each test data set are compared with numerical models. An alternative contact-less testing technique is used that makes use of particle velocity sensors and allows removing mass loading effect in modal models. Comparisons are provided for real test cases such as a lightweight thin plate and a small car turbine.

INTRODUCTION Modal analysis is a worldwide-used methodology that allows fast and reliable identifications of system dynamics in complex structures. In the last decades several methods have been developed in the quest to improve the accuracy of modal models extracted from test data and to enlarge the applicability of modal analysis in industrial context. In this respect, the recently developed PolyMAX algorithm makes the identification process even faster and more reliable paving the way to automatic modal parameter extraction also for difficult cases such as high-order or highly damped systems with large modal overlap thus enhancing the exploitability of modal testing data. However, the process of converting modal test data into reliable modal models suffers for some limitations related to testing techniques and theory assumptions. In theory, one of the most stringent hypothesis for modal analysis methods to apply is that the structure must have a dynamic linear behaviour in the field of experimental observation, which can briefly resumed as the property of exhibiting a constant proportional relationship between the amplitudes of dynamic responses and applied excitations. Good technical practice makes it that the field of normal operating conditions for a structure be included in the its field of linearity but critical operating conditions - such as large temperature variations - may lead to a breach of linearity a thus reduce severely the reliability of modal models. Another limitation to the usability of test data derives form the difficulty of testing large or geometrically complex structures, especially when this is coupled to limitations in the testing equipment such as the number of available sensors or acquisition channels. In these cases a so_______________________________________________________________________________ Managing Uncertainty in Noise Measurement and Prediction

Symposium Le Mans (France) 27-29 June 2005

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called “multi-patched” testing approach is followed that allows using the same set of sensors and/or channels in several consecutive test runs, each corresponding to a limited number of measuring locations on the structure. The test lasts once all runs have been completed, i.e. each measuring point has been covered at least once in the acquisition process. Such a technique has however some drawbacks as it may lead to the introduction of discrepancies in the data measured in different runs. As an example, in case of MIMO testing using shaker excitations, relocating sensors from one run to another requires the test engineer to manipulate the structure and this may compromise the shaker connection, especially in case of lightweight structures tested under free-free boundary conditions. Any change in the shaker connections may introduce a variation of the reference signal used for the computations of FRFs. The result is that different runs may have different reference scaling factors leading to some variation in the information content carried out by FRF as computed in different patches. Analogously, concentrating sensors in a small area over the structure may cause some patches to be affected by mass loading effects, which again results into variations of FRF contents and correspondingly into inconsistencies amongst different runs. Those variations and inconsistencies lead to uncertainties in the modal model extracted merging all runs together. This paper presents the results of a systematic study carried out to assess the impact of data uncertainties as issued from multi-patch vibration tests on the quality of the extracted modal models. The study makes use of a large amount of test data as gathered through several testing sessions using a variety of different testing techniques, modal design tools that allows predicting the impact of structural variations in the modal models – such as mass loading effect - on data consistency and pre-test techniques. Finally a new modal testing technique is presented that uses contact-less particle velocity sensors and allows identifying very accurately the modal model.

THE MASS LOADING EFFECT Experimental data are often affected by systematic errors induced by the experimental set-up or more specifically by the data acquisition instrumentation. A systematic error frequently encountered in modal testing is the mass loading effect. This error is generated by the mass of the transducers that are placed over the test article to capture the structural response to controlled excitation. Transducers mass adds up to the structural mass and cause a modification of system parameters that results in incorrect estimation of the structural eigenfrequencies extracted from experimental data by curve fitting algorithms. This effect is obviously as much pronounced as lighter is the test article, it is therefore on very lightweight structures that the present experimental research work concentrates. A simplified analytical formulation for the sensors mass loading effect can be derived from the equation relating the dynamic stiffness Z 0 of a given system with the modified stiffness Z m of the same system after an additional mass mh is added:

Z m = Z 0 − mhω 2

(1.1)

Equation 1.1 shows the functional dependencies of the relevant parameters appearing in the phenomenon. In general, mass loading (i.e. the added mass mh ) induces a reduction of the measured system’s dynamic stiffness hence it shows up experimentally as a shift of the system eigenfrequencies to lower frequency values. In parallel the 1.1. shows that mass loading is frequency dependent and this directly limits the frequency range of usability of a given sensor: a heavy sensor lead to unreliable data at high frequency ranges. Finally, mass loading is also very sensitive to ratio between local dynamic stiffness and transducer mass. Such local dynamic stiffness is the stiffness of the modally active part of the structure [2] so that sensors placed at modal nodes

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will not suffer from mass loading while sensors placed at anti-nodal location will exhibit large mass loading. In the endeavour to extrapolate general rules and a comprehensive analytical treatment of mass loading, a number of case-specific approaches have been developed and are extensively reported in literature. One of the first attempts to systematically treat the mass loading effect resulted into the SMURF method (Structural Modification Using experimental Response Function) as introduced by Klosterman in the early 70’s, which allows deriving a formula to account for mass loading effect in the computation of the local accelerance [1][2][4]. Using the Sherman-Morrison formula for a more efficient matrix inversion, Cakar e Salinturk [3] derived a correction method for mass loading that applies the idea of simulating system mass variations by adding to the real system negative masses matching to the sensor mass. However, none of those treatments covers suitably the specific problems of multi-patched modal tests on very lightweight structures, where inconsistencies may arise due to bad placement of sensors or to slight modifications induced in the test set-up occurring when moving sensors to consecutive patch locations. In such cases, the impact of mass loading on the FRFs may remarkably vary for each of the test runs. The resulting curve fit must then rely upon sub-sets of not fully consistent FRFs, leading to a difficult interpretation of stabilization diagrams and eventually into uncertain modal models. The usual validation techniques applied in modal analysis to verify the quality of the modal model such as mode shape animation are not much helpful: different modal models look pretty similar and quite often mode shapes are very complex [8]. From an experimental point of view, the most advisable approach consists of uniformly distributing sensors over the structures such as to minimize the effect of mass loading induced structural modification on the test article. This is however particularly challenging in case of multi-patch test, given that such a uniform distribution can barely be kept constant in all patches without affecting either the global mass of the structure or the test efficiency (e.g. redundancy in test data). Moreover, this approach is not beneficial for very lightweight structures, as the transducers mass will significantly change the structural parameters and therefore the modal models. This specific problem is addressed in the next paragraphs using two real application cases such as a thin aluminium plate and a very small car turbine that is characterized by very high frequency first blade eigenmodes.

EXPERIMENTAL ASSESSMENT OF SENSORS MASS LOADING An intensive test campaign has been carried out on two test articles of industrial relevance. The first deals with a thin aluminium plate, the second with a very small car turbine. The test set-up used consisted of a set of impact-hammers and a set of very light accelerometers, the smallest having a mass of only 0.15 grams (figure 1).

Figure 1: micro-accelerometers and micro-hammer used for the test

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A novel contact-less approach in modal testing has also been undertaken that uses Microflown sensors [10]. These sensors are specially conceived for measuring acoustic intensity, as they integrate in a unique casing a hot-wire particle velocity sensors and a very small pressure transducer (figure 2). The use of this sensor proved successful for modal testing type of activity as they allow acquiring directly point mobility hence result into a more numerically stable data processing of the curve fitting algorithms.

Figure 2: the Microflown 3D p-u sensor. The aluminium plate Several test have been carried out on the aluminium plate, these includes a modal test – roving hammer – a multi-patch modal testing and a roving hammer test using a particle velocity as response. In addition a numerical model was built for both the thin plate and the car turbine. Numerical models are compared with the best test results. Figure 3 shows the aluminium plate and the corresponding measurement grid used in all tests. These consist of comparison of three different modal tests: a multi-patch impact hammer modal test performed using special care in uniformly distributing sensors over the plate; a modal test performed using only 2 accelerometers in a fixed location and roving the impact hammer over all measurement points; a roving hammer test using particle velocity sensor as response and placing the probe at the same two measuring points of the test with 2 accelerometers.

Figure 3: Aluminium plate: test set-up and measurement grid Table 1 reports the results obtained with the multi-patch test with accelerometers. Only 2 patches were used, such as to minimize the impact of mode merging and to try focusing on purely data acquisition induced uncertainties.

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Table 1: list of modes extracted form multi-patch test on the aluminium plate Mode

Freq (Hz)

Damp.

1 2 3 4 5 6 7 8

58.425 73.049 146.963 159.675 237.974 255.002 279.923 312.949

1.18% 2.04% 2.02% 1.25% 2.07% 2.00% 1.45% 1.62%

Successively a second modal test was performed using only 2 accelerometers. The resulting eigenmodes are reported in table 2 and show the substantial underestimation of eigenfrequencies in the multi-patch test. Of particular relevance is also the difference observed in modal damping. This effect is somehow expected; multi-patch type of test uses more sensors and therefore affects a lightweight structure much heavier than the test using only two accelerometers. In this second test, FRF of very good quality (form a purely system dynamics point of view) were measured. Figure 4 shows the FRF, where the rigid body modes appear at sufficiently low frequency and well isolated form the first eigenmode.

Table 2: list of modes extracted from 2 accelerometers test on the aluminium plate Mode

Freq [Hz]

Damp.

1 2 3 4 5 6 7 8

66.096 86.592 180.187 191.745 305.085 321.945 355.122 369.586

0.39% 0.49% 0.29% 0.23% 0.37% 0.47% 0.39% 0.26%

Figure 4: Rigid body modes for the aluminium plate in the case of 2 accelerometers modal test

A third test was carried out using particle velocity sensor located at the same position as for the 2 accelerometer test and roving the impact hammer over the plate. The relevance of this test is given by the fact that the test technique is contactless. In theory, the test results are equal to the case of a multi-patch testing executed by roving the sensor and hammering always at the same location.

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Table 3: list of modes extracted from multi-patch test using particle velocity sensor Mode

Freq [Hz]

Damp.

Mode

Freq [Hz]

Damp.

1 2 3 4

68.798 90.183 190.433 195.205

0.24% 0.57% 0.37% 0.07%

5 6 7 8

318.375 334.672 369.987 381.819

0.80% 0.33% 0.34% 0.35%

In this case the differences with the previous test case are much more limited. In particular, the damping is in the same order of magnitude, while in the multi-patch case, modal damping is remarkably higher. As for eigenfrequencies, differences are small and consistently accounting for slightly higher values in the contact-less test case. In order to better illustrate the differences between the last two test cases, figure 5 shows the sum of all FRFs for the two cases. The red curve refers to the particle velocity based measurements, the green curve to the 2 accelerometers test. It can be observed that even two very small and light accelerometers are sufficient to move eigenfrequencies to a lower value. This frequency shift effect is more pronounced at higher frequency and it results from the mass loading effect induced by the 2 accelerometers’ mass.

Figure 5: Microflown (red) vs. 2 accelerometers (green)

Figure 6: Stabilization diagrams:particle velocity (left), 2 accelerometers (mid), multi-patch (right) Another interesting aspect of this experimental comparison is the effect of mass loading on the quality stabilization diagram. Figure 6 shows the stabilization diagrams of the three different tests and it shows comparatively the relative easiness of selecting a good set of system poles. Even though the new and high performing PolyMAX algorithm was used, the stabilization diagram resulting of multi-patch test is less clear than the two other tests. On the contrary, PolyMAX remarkably reduces differences between particle velocity based fit and 2-accelerometer based fit.

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Finally a Finite Element model was developed to compare test results in the case of the aluminium plate. The results are reported in table 4 and show a perfect fit of the new contact-less technique to the numerical model. Mode shape animation results also manifestly better for particle velocity sensors based test because modes shows up almost identical to FEM mode shape results.

Table 4: Modal model comparison: FE model vs. experimental (particle velocity sensor) modes Mode

FEM [Hz]

Microflown [Hz]

∆Freq. [Hz]

∆Freq. [%]

1 2 3 4 5 6 7 8

68.2 87.8 189.9 192.6 315.5 331.9 366.8 383.0

68.798 90.183 190.433 195.205 318.375 334.672 369.987 381.819

-0.6 -2.4 -0.5 -2.6 -2.9 -2.8 -3.2 1.2

-0.9 -2.7 -0.3 -1.4 -0.9 -0.8 -0.9 0.3

Mass loading due to sensors Cabling An additional test case was carried out to experimentally assess the impact of mass loading induced by sensors cabling. Figure 7 illustrates the different location adopted in two modal tests. The first distribution (A) shows a uniform spreading of sensors and connecting cables over the test article. In the second test (B), connected cables are located all on the same side of the plate.

Figure 7: sensor distribution for cabling mass loading effect assessment

Figure 7: sum of FRFs. Test configuration A (red) and B (green) The resulting modal models are clearly different, the sum of FRFs shows that for each mode shape, the corresponding eigenfrequency shifts to lower values as result of sensor cables mass loading.

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Table 4: list of modes shapes and corresponding MAC Config. A

Config. B

Mode

Freq.[Hz]

Damp.

Freq.[Hz]

Damp.

MAC

1 2 3 4 5 6 7 8 9

58.705 73.474 158.656 161.987 250.730 272.827 284.475 316.158 -

1.22% 1.96% 1.70% 1.18% 2.43% 0.87% 1.64% 1.98% -

58.360 72.843 156.317 159.819 242.457 263.259 282.671 317.046 374.045

1.54% 2.07% 1.18% 1.42% 4.05% 1.73% 0.94% 1.05% 2.40%

95.340 97.877 97.860 96.453 84.192 88.368 82.169 90.966

APPLICATION CASE 2: CAR TURBINE In a second test campaign a 9 blades car turbine of 56,6 g weight was tested with the purpose to identify and discriminate the first eigenmode of each blade separately (figure 8). The problem is not satisfactory solved with FE approach as the model representation introduces geometrical and mass distribution symmetry, which is not satisfied on the actual turbine. The test challenge is to make sure that mass loading of accelerometers is kept under acceptable limits and that an adequate excitation level is provided with the micro hammer (figure 1). On the other hand, the very high frequency of the first mode blades makes it very difficult to achieve a high frequency excitation with a micro-hammer and to detect a good level response due to accelerometer frequency response range limits. To this aim very small hammer and very light accelerometers (0.15 g weight) are used.

Figure 8: the car turbine and the micro accelerometers in the test set-up

Figure 9: first natural frequencies of the turbine blades

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The test technique used is the standard modal testing, with a multi-patch approach consisting of using one accelerometer as driving point in a fixed location and a moving accelerometer that measures the structural response on one blade only for each patch. The experimental test shows that the blade first mode eigenfrequencies are all included in a frequency range between 20 kHz and 26 kHz (figure 9). Nevertheless the test results in 15 eigenfrequencies (Table 5) that are found in the frequency range of pertinence and this makes it more difficult to uniquely identify each mode shape. Mode shape animation does not provide much help.

Table 5: list of modes shapes in the blade first mode frequency range Mode 1 2 3 4 5 6 7 8

Freq. [kHz] 21.927 22.617 22.687 23.570 23.698 23.762 23.921 24.087

Damp. 0.09% 0.04% 0.04% 0.10% 0.23% 0.81% 0.04% 0.13%

Mode 9 10 11 12 13 14 15 -

Freq. kHz] 24.323 24.495 24.613 24.770 24.892 25.156 25.200 -

Damp. 0.05% 0.08% 0.98% 0.04% 0.07% 0.06% 0.08% -

A second test was then carried out using particle velocity sensor (figure 10).

Figure 10: multi-patch using particle velocity sensors The results are amazingly improved as the identification algorithms extract only 9 eigenmodes.

Table 6: list of modes shapes in the blade first mode frequency range (particle velocity sensor) Mode 1 2 3 4 5

Freq. [kHz] 21.974 22.876 23.762 24.035 24.157

Damp. 0.02% 0.02% 0.02% 0.02% 0.02%

Mode 6 7 8 9 -

Freq. [kHz] 24.237 24.598 24.980 25.242 -

Damp. 0.02% 0.02% 0.02% 0.02% -

Figure 10: Stabilization diagrams: particle velocity sensors (left) vs. accelerometers (right)

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The higher number of poles identified in the first test case is due to mass loading effect generating frequency shifts that vary from one patch to another. When all patches are put together in the sum of FRF, this exhibits several pseudo-double modes generated by the mass loading induced frequency shift. In the case of contactless measurements, the data analysis allows easily identifying all blade first modes, even though self tuning effect are also present that excites higher blade modes whose frequency coincides with the first modes of some other blade.

CONCLUSIONS An experimental evaluation of the impact of data uncertainties on modal models extracted is discusses thought two real applications cases. Focus is given to data uncertainties induced by mass loading effect in multi-patch modal tests. For very lightweight structures, standard modal testing techniques induce sensor mass loading and lead to incorrect modal models. An alternative contactless testing technique is introduced that makes use of particle velocity sensors and allows achieving very high accuracy in the modal models extracted. Comparisons with numerical models confirm the superior quality of modal models extracted with contactless particle velocity sensors.

ACKNOWLEDGMENTS This research was carried out in the frame of the EC project AMPA (Automatic Measurement Plausibility and quality Assurance). The support of the EC is gratefully acknowledged.

BIBLIOGRAPHY [1] Ashory, M. R., Correction of mass-loading effects of transducers and suspension effects in modal testing, Proceedings of the 16th IMAC, Leuven pagg.815-828, 1998 [2] Baldanzini, N. & Pierini, M, An assessment of transducer mass loading effects on the parameters of an experimental statistical energy analysis (SEA) model, Mechanical Systems and Signal Processing 16, p. 885-903, 2002 [3] Cakar, O. & Sanliturk, K. Y., Elimination of transducer mass loading effects from frequency response functions, Mechanical Systems and Signal Processing 19, p. 87-104, 2005 [4] Decker, J. & Witfeld, H., Correction of transducer-loading effects in experimental modal analysis, Proceedings of the 13th IMAC, Nashville, p. 1604-1608, 1995 [5] Dossing, O., Prediction of transducer mass-loading effects and identification of dynamic mass, Proceedings of the 9th IMAC, Firenze, p. 306-311, 1991 [6] Silva, J. M. M., Maia, N. M. M. & Ribeiro, A. M. R., Some applications of coupling/uncoupling techniques – Part 1: Solving the mass cancellation problem, Proceedings of the 15th IMAC, p. 1431-1439, 1997 [7] Mc Connel, K. G. & Cappa, P., Transducers inertia and stinger stiffness effects on FRF measurements, Proceedings of the 17th IMAC, Orlando, p. 137-145, 1999 [8] Van Der Auweraer, H., Leurs, W., Mas, P. & Hermans, Modal parameter estimation from inconsistent data sets, Proceedings of the 18th IMAC, p. 763-771, 2000 [9] Heylen, W., Lammens S., Sas, P., Modal Analysis Theory and Testing, Katholieke Universiteit Leuven, Leuven, 1995 [10]

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