COMPARISON OF 3D LASER VIBROMETER AND ACCELEROMETER FREQUENCY MEASUREMENTS

Transcription

1 Proceedings of the IMAC-XXVII February 9-12, 2009 Orlando, Florida USA 2009 Society for Experimental Mechanics Inc. COMPARISON OF 3D LASER VIBROMETER AND ACCELEROMETER FREQUENCY MEASUREMENTS Pawan Pingle, John Sailhamer, Dr. Peter Avitabile Structural Dynamics and Acoustic Systems Laboratory University of Massachusetts Lowell One University Avenue Lowell, Massachusetts ABSTRACT Laser techniques are very popular due to the non-contacting nature of this measurement device. Accelerometer measurements are also widely used in many applications but suffer from potential mass loading effects. Each technique has its own benefits and drawbacks. Some comparative measurements are made using both of these devices to show some of the strengths and weaknesses of each, especially when measuring in a 3D environment. A variety of different measurement scenarios are presented. INTRODUCTION Structural dynamic testing approaches have been employed for decades to better understand or identify dynamic characteristics. In particular, experimental modal analysis has been commonly employed and is widely used in many industries and for many applications. The experimental modal analysis technique relies on the accurate measurement of frequency response functions to describe the input-output characteristics of the structure. These measurements are then used to extract frequency, damping and mode shapes through modal parameter estimation algorithms (curve-fitting) to characterize the structure. The accuracy of the measured frequency response functions are especially important when performing frequency based substructuring (impedance modeling, admittance modeling) or when correlating test data with a finite element model. In such cases, the measured functions must be of the highest quality. As far as correlation of analytical models with measured data, Avitabile [1] showed that small errors in measured frequency response functions contaminate the mode shapes and have a significant effect on the overall correlation results (MAC and POC). Such errors could be assessed using the correlation tools developed. Butland [2] studied the problem, confirming that, the data could be smoothed by treating poorly measured degrees of freedom for each of the individual modes as outliers to the data smoothing process. Butland further developed an approach (VIKING) to process the data and smooth the variance observed in the measurements. In that work, Butland clearly showed that the results were vastly improved over the results where no smoothing was utilized. While developing frequency based substructured models, many studies have shown [3,4,5] that the variations in the measured functions play a very critical role in the final results. Carne [5] showed that small variations in the drive point frequency response function could be observed in a measured function and needed to be smoothed or removed from the contaminated functions to get better results. Wirkkala [4] showed that while pure analytical frequency response functions produced accurate system models, the measured counterpart frequency response functions suffered from measurement accuracy. Nicgorski [3] extended Wirkkala s work and identified typical measurement issues and studied their effects on the overall system model results. Nicgorski further identified cross axis sensitivity as a very significant contributor. In Nicgorski s work, these measurement contaminants were mitigated with smoothing functions and the resulting system model results were vastly improved, clearly showing that the typical measurement contaminants needed to be properly addressed before using any measured functions.

2 In all of these previous studies, accelerometers were used for the development of the measured frequency response functions. Accelerometers are typically used for this type of work due to cost and availability of hardware. However, one common criticism of accelerometers is that they tend to mass load the structure thereby introducing some error to the measured functions. Another common criticism is that the accelerometers do not measure at the exact point on the structure (due to their physical construction) and have cross axis sensitivity issues that will cause some slight errors in the measurements. However, many have used lasers as an alternative to the measurement of frequency response functions. Lasers are stated to be very accurate and do not physically affect the structure due to the non-contacting nature of the laser measurement. In the first use of lasers, the measurements were restricted to only 1D measurements where response normal to the surface was the prominent feature of interest. Recently, the advent of the 3D scanning laser vibrometer has opened the door for the possibility of 3D measurement capability. This new measuring capability has offered tremendous possibilities in the areas of frequency based substructuring and correlation of analytical models with test data. In this paper, some comparisons will be made between traditional accelerometer measurements and a 3D scanning laser vibrometer on a simple structure that has very directional modes. An analytical model of the structure is also available for comparison of the results from the two measuring approaches; this structure has well known modes and has been used for several other studies. IMPETUS FOR STUDY During routine testing with the laser, a comparison was made to an accelerometer. In this measurement, the laser was located at the same location as the accelerometer to obtain a comparison of the frequency response function (FRF) and coherence for a typical measurement. Figure 1 shows the resulting comparison of the coherence (left) and the FRF (right); the laser measurement is in the upper trace and the accelerometer is in the lower trace. For most of the 5KHz frequency range, the measurement looks very acceptable. But there is a lot of variation and the measurement from the laser is particularly poor in the KHz range where the FRF is very poor along with the corresponding coherence. As a result of this measurement, a study was performed to investigate some of measurements with different set up conditions. Figure 1- Coherence and FRF Comparing Laser (top) and Accelerometer (bottom) CASES STUDIED Several cases are studied as part of the work presented here. First an analytical model is shown to identify the typical modes expected from the actual test structure. There are six main cases studied and are summarized as: Case 1 Laser Normal to Surface of Structure a) Test on Untreated Structure b) Test on Structure Treated with Magnaflux c) Test on Structure Treated with Reflective Tape Case 2 Laser Skewed Relative to Surface of Structure Case 3 Laser Normal to Surface of Structure using only 8 laser points Case 4 Conventional Test on Structure using Eight Tri-axial Accelerometers Case 5 Comparison between LDV and Tri-axial Accelerometer Modal Data Case 6 Comparison between LDV and Tri-axial Accelerometer Measurements (FRF Comparison)

3 Structure Description & General Testing Performed A general structure is used for the description of the test article. This structure is referred to as BU (base upright) and is made of 3/8 thick aluminum plate; the base plate is 24x24 and the upright is 24x36. The structure is rigidly bolted to the floor at four locations. A finite element model is available and has been shown to be very well correlated to other measured test data from previous studies; the average frequency difference is less than 2.5% and the minimum MAC is greater than 0.97 for the first six modes of the structure confirming that the model is a very good representation of the structure. The structure model and several mode shapes are shown for reference in Figure Hz 71 Hz 78 Hz 109 Hz 158 Hz 270 Hz 304 Hz 350 Hz Figure 2 - Structure Model and Mode Shapes for Structure under Study. For the experimental testing, shaker excitation was provided. The excitation was pseudo random over a 400 Hz bandwidth with 1600 lines of spectral resolution with sufficient averaging (30 averages) to obtain adequate coherence in the measured frequency response functions. For the accelerometer testing, 8 tri-axial accelerometers were permanently mounted at the locations shown in Figure 3. For the 3D laser testing, 85 measurement points were obtained with laser locations also seen in Figure 3. The structure is also shown in the figure along with the two laser orientations used for the cases studied. The shaker was located at 45 degrees to the three major axes such that all modes were excited during the test. Figure 3 - Structure Accelerometer and Laser Measurement Locations with Structure Photo.

4 Case 1 - Laser Normal to Surface of Structure Shaker excitation was applied such that modes up to 400 Hz in all the three directions (X, Y and Z) are excited. The 3D Laser Doppler Vibrometer (LDV) was set such that the laser was located essentially normal to the surface of the structure; the laser beams are basically perpendicular to the surface of the structure. This is shown in Figure 3 with the normal laser configuration shown on the left portion of the figure. Data at 85 points on the structure was collected. Modal parameter estimation was performed using LMS Cada-X and Test.Lab [6] and modes were extracted. There were three separate surface treatments that were applied to the structure for evaluation of data. These were the untreated surface, the surface treated with a magnaflux spray commonly used for this type of test and the surface treated with highly reflective tape typically used. (While there were many other surface treatments studied, they are too numerous to include here; the data included presents a good range of results obtained.) For each of the surface treatments studied, the modal parameters extracted were used for correlation with the reference finite element model. The correlation was performed using the FEMtools software [7] to generate the MAC and POC correlation results. Laser data was collected using the Polytec Laser Vibrometer system [8]. Case 1a - Test on Untreated Structure In Case 1a, the 3D LDV was used to test an untreated structure with no reflective tape or coating used. While the signal for the laser vibrometer was not optimal, the signal was sufficient to collect data and identify FRFs for the structure. The MAC and POC results are shown in Figure 4. The MAC shows poor correlation for several of the major modes of the structure (modes 3, 5, 6 and 7). The resulting POC values are much better overall when compared to the MAC values. However, there are quite a few off-diagonal terms that are generally not considered acceptable for general correlation purposes. The main reason for the poor correlation is most likely due to the untreated surface not providing appropriate reflectivity. M A C File FEA Hz EMA Hz P O C File Figure 4 - Mode Shape Correlation for Untreated Surface (Case 1a)

5 Case 1b - Test on Structure Treated with Magnaflux In Case 1b, the 3D LDV was used to test the structure with a light coating of magnaflux to increase the reflectivity. The signal for the laser vibrometer was very good and sufficient to collect data. The MAC and POC results are shown in Figure 5. The MAC improved significantly after treating the surface with magnaflux and the same is true for the POC. While the off-diagonal terms are better than the case with the surface untreated, the off-diagonal terms are still relatively large. M A C File FEA Hz EMA Hz P O C File Figure 5 - Mode Shape Correlation for Magnaflux Treated Surface (Case 1b)

6 Case 1c - Test on Structure Treated with Reflective Tape In Case 1c, the 3D LDV was used to test the structure with reflective tape attached at 85 scanning locations. The signal for the laser vibrometer was very good and sufficient to collect FRF data. While the attachment of reflective tape to all of the measurement points is tedious, the resulting reflectivity provides better results overall. The MAC and POC results are shown in Figure 6. The MAC and POC are the best of the sets of results for the LDV data considered. While the diagonal terms are improved, some of the off-diagonal terms are still not as low as would be desired or expected for this structure. M A C File FEA Hz EMA Hz P O C File Figure 6 - Mode Shape Correlation for Reflective Tape Treated Surface (Case 1c)

7 Case 2 - Laser Skewed Relative to Surface of Structure In Case 2, the 3D LDV was used to test the structure with reflective tape attached at 85 scanning locations but the laser was oriented at an angle skewed relative to the structure. This was done to determine if some of the poor correlation was a result of the extremely directional modes in the structure. The laser was oriented with approximately a 30 degree angle from the normal and approximately a 20 degree angle in elevation. This is schematically shown in Figure 3 on the right side of the figure. Reflective tape was used at 85 measurement locations to obtain the best possible signal for the laser. The MAC and POC are shown in Figure 7. In general, all of the terms from the MAC and POC are just slightly less than those where the laser was located normal to the surface of the structure; the off-diagonal terms are also not as good as those of the previous case (Case 1c). M A C File FEA Hz EMA Hz P O C FIle Figure 7 - Mode Shape Correlation for Reflective Tape Treated Surface with Skewed Lasers (Case 2)

8 Case 3 - Laser Normal to Surface of Structure using only 8 laser points Because the ultimate comparison will be with the 8 tri-axial accelerometer locations, the laser data from Case 1c was decimated to include just the 8 locations corresponding to the accelerometer measurement locations. Case 1c was chosen because it was the best set of results obtained. The MAC and POC for these 8 points are shown in Figure 8. These results need to be compared to Case 1c. In reviewing these results, the MAC and POC are very similar to the results of Case 1c. This implies that the 8 point laser subset produces essentially the same results as the 85 point laser test. Therefore, the use of only 8 points does not seriously degrade the overall results obtained when compared to the larger set of 85 points. M A C File FEA Hz EMA Hz P O C FIle Figure 8 - Mode Shape Correlation for Reflective Tape Treated Surface with 8 Laser Points (Case 3)

9 Case 4 - Conventional Test on Structure using Eight Tri-axial Accelerometers In Case 4, eight tri-axial accelerometers were used to test the structure. These 8 locations correspond to 8 of the 85 laser measurement points. The MAC and POC for correlation to the finite element model is shown in Figure 9. The results are very similar to the laser results of Case 3 but with slightly improved results; this is best seen in reviewing the off-diagonal terms of the POC matrix which are generally lower for this case when compared to the laser results of Case 3. M A C Acc FEA Hz EMA Hz P O C Acc Figure 9 - Mode Shape Correlation for 8 Accelerometer Points (Case 4)

10 Case 5 - Comparison between LDV and Tri-axial Accelerometer Modal Data The comparison between the 8 point laser correlation to the finite element model and the 8 point tri-axial accelerometer results shows comparable results. The average diagonal term for the both cases and the average off-diagonal term is shown in Table 1. Clearly, the accelerometer data is better than the laser data when considering both the diagonal and off-diagonal terms for the correlation to the finite element model. From these cases studied, both the accelerometer and 3D LDV (treated with reflective tape) produce good mode shape results for correlation to the finite element model. However, while the correlation results are similar, the most significant difference will be seen in the comparison of the actual FRF measurements shown next. Table 1 - Comparison of LDV and Accelerometer POC Terms Type of POC terms Laser Data (Magnaflux) (Reflective Tape) Accelerometer Data Average Diagonal Average Off-Diag Case 6 - Comparison between LDV and Tri-axial Accelerometer Measurements (FRF Comparison) The frequency response functions are compared for several of the 3D laser cases (Case 1a, Case 1c, Case 2) studied along with the accelerometer data. The x, y and z directions are all compared separately for Point 3 on the structure as seen in Figure 10. Clearly, the x and y direction FRFs and coherence are very noisy for all of the laser measurements whereas the accelerometer is vastly better. This is most noticeable in regions away from the resonances of the system. The best of the FRF and coherence measurements is for the z direction which is the direction aligned with the laser beams. All of the laser measurements are very similar for the z direction and compare reasonably well with the accelerometer. The only differences in amplitude of the FRF are related to the fact that the accelerometer is mounted on the surface and there is a slight offset with respect to the actual surface where the laser measures due to the physical size of the accelerometer. The laser measurements are most accurate for the FRF that is most aligned with the direction of the laser beams. The other two directions that are essentially perpendicular to the normal direction are not very accurate representations of the FRF over the whole frequency range. While the resonant peaks are reasonable, the majority of the frequency response is unusable for any frequency based description of the structure. In addition to this one measurement reviewed for Point 3, a waterfall plot for all 8 points is also provided for the x, y and z directions for the accelerometer and the best laser measurement (Case 1c with reflective tape applied to the structure). The FRF measurements are shown in Figure 11 and the coherence functions are shown in Figure 12. For both figures, the accelerometer measurements are shown in the upper portion of the figure and the laser data is shown in the lower part of the figure. From these two figures, the data for the accelerometer is very obviously much better than the data from the laser system. This is especially true for the x and y directions but is also seen to some degree for the z direction. Clearly, the FRFs obtained from the LDV would be inadequate for use in any frequency based system modeling approaches (impedance modeling, admittance modeling, etc). Some type of data smoothing (similar to that presented in Reference 2 and 3) would be needed in order to use these measurements for frequency based system modeling applications.

11 Figure 10 - FRF (upper) and Coherence (lower) Comparison for Point 3 (Case 6)

12 Figure 11 - FRF Comparison for All Points (Case 6) Figure 12 - Coherence Comparison for All Points (Case 6)

13 SUMMARY Measurements were made using a 3D Laser Doppler Vibrometer and compared to traditional accelerometer measurements. Correlation to a finite element model was performed as a basis for comparison. In general, the laser results were comparable to the accelerometer results for correlation studies performed where mode shapes were used for comparison. However, overall, the accelerometer results were better than the laser results for the descriptions of modes used for the correlation evaluation. The most significant area of difference was related to the comparison of the actual FRF measurements. The accelerometer measurements were better than the 3D Laser Doppler Vibrometer measurements for all cases studied. This was particularly true for the laser measurements that were obtained that were perpendicular to the main sensing direction of the 3D laser beams. The laser measurement in the main direction of the 3D laser beam was the best of all the FRFs collected and very similar to that obtained from the accelerometer. In order to obtain the best possible results for the laser, reflective tape was required to be used as a treatment to the structure surface to obtain good reflectivity. The 3D Laser Doppler Vibrometer allowed for accurate identification of mode shapes and allowed for non-contacting measurements at many points but required surface treatment. Overall, in all cases studied, the traditional accelerometer produced overall better measurements when compared to the 3D laser vibrometer measurements obtained. REFERENCES 1 Avitabile,P., Modal Model Correlation Techniques, Doctoral Dissertation, University of Massachusetts Lowell, Butland, A. A Reduced Order, Test Verified Component Mode Synthesis Approach for System Modeling Applications, Master s Thesis, University of Massachusetts Lowell, January Nicgorski, D., Investigation on Experimental Issues Related to Frequency Response Function Measurements for Frequency Based Substructuring, Master s Thesis, University of Massachusetts Lowell, January Wirkkala, N.A., Development of Impedance Based Reduced Order Models for Multi-Body Dynamic Simulations of Helicopter Wing Missile Configurations, Master s Thesis, University of Massachusetts Lowell, April Carne, T. G., Dohrmann, C. R., Improving Experimental Frequency Response Function Matrices for Admittance Modeling, Proceedings of the Twenty-Fourth International Modal Analysis Conference, Saint Louis, Missouri, CADA-X Modal & Test.Lab Software, Leuven Measurement Systems, Leuven, Belgium 7 FEMtools 3.0 Dynamic Design Solutions, Leuven, Belgium 8 Polytec Scanning Laser Doppler Vibrometer, Polytec Optical Measurement Systems 9 MATLAB 7.0 The MathWorks, Natick, Massachusetts