On the accuracy reciprocal and direct vibro-acoustic transfer-function measurements on vehicles for lower and medium frequencies

On the accuracy reciprocal and direct vibro-acoustic transfer-function measurements on vehicles for lower and medium frequencies C. Coster, D. Nagahata, P.J.G. van der Linden LMS International nv, Engineering Services Interleuvenlaan 68; B-3001 Leuven, Belgium 1 Introduction Diagnosis and reduction of structure borne sound in complex machinery, installations and vehicles has become much more feasible and predictable through the use of source-transfer testing; transfer path analysis. The forces are measured, or estimated, at interfaces and the transfer from the forces to the sound pressure is measured. The combined information allows contribution analysis and also shows which part of the system is weakest and can be improved by modification. On road vehicles transfer part analysis was first mostly used for the 20 to 200 Hz frequency range for low order engine effects. Now, derived techniques like inverse force identification, hybrid modeling en parameterized force identification (OPAX) are used for frequencies up to 1000 Hz and sometimes higher for tire-road excitation, pumps, gear whines, etc. The extension to higher frequencies maintaining correct and useful transfer path analysis is not evident. We will not discuss the force identification issues. But, one reason is the much more demanding instrumentation for the vibro-acoustic transfer functions. Especially on complete vehicle, reciprocal transfer-function tests have a major advantage in required effort and in positioning accuracy around mounts. Acoustic excitation at the ear location, and response accelerometers around the mounts, allow more freedom in positioning the sensors close to mount center, and it is more feasible to surround mounts with sensors. Recently reciprocal measurements have become more important because of the new parametric force identification (OPAX), which is based on operational data and complete vehicle reciprocal FRF measurements. The focus of the investigation of the accuracy of the transfer functions is on angular sensitivity with direct and reciprocal excitation and on the radiation and diffraction of the sound source in comparison with the ear of a person, and in comparison with a microphone. In-vehicle reciprocal vibro-acoustic FRF s are usually measured using a sound source located on the front driver or passenger seat. The source under investigation in this study is the LMS low frequency volume source. This source for the 20 to +- 1000 Hz frequency range is commonly used in the industry for vehicle vibro-acoustic testing. Any low frequency source with a sufficient noise level requires space and will therefore diffract the sound field. This influences the omni-directionality of the source, especially in the near field. The diffraction behavior of the LMS-Qsources low frequency volume source is specific because it aims to include the average human body diffraction at low frequencies, potentially providing a better approximation of the vibro-acoustic FRF to a human ear. In order to communicate a suggested approach to best handle recipr ocal vibro-acoustic measurements it is required to understand which boundary conditions are typically sensitive to achieve reciprocity. To support experimental sensitivity study and validation, both a test based approach and CAE approach by the mean of Boundary Elements Models have been performed. 3873

3874 PROCEEDINGS OF ISMA2010 INCLUDING USD2010 2 Methodology background Several existing sound decomposition techniques such as Transfer Path Analysis (TPA) for vibro-acoustic phenomena or Airborne Source Quantification (ASQ) for air borne phenomena can be considered when the origin of noticeable Sound Pressure needs to be identified. The classical TPA approach is used in order to analyze the noise contribution generated by the driveline active forces at driveline mounts that propagates inside the vehicle cabin at a given receiver location. Being decomposed into several discrete interface excitations, the noise or vibration problem is expressed as the sum of all discrete contributions due to individual paths. P = P = P r : identified total sound pressure at receiver location r (Pa) r i ri i PF F. H ( Pa) P ri : sound pressure contribution at receiver r due to interface force i (Pa) F i : single direction contact force i at a mounting (N) H ri : vibro-acoustic transfer between force i and sound pressure at r (1/m²) i ri (1) The summed effect of the discrete interface excitations in TPA can reproduce the level of the total measured sound pressure as well as give insight about the relative contribution of each force or each path is critical to the total response. The separation into loads and paths is the key to identify dominant causes, estimate improvement potential and propose solutions. Even though the test approach to build a conventional TPA is well know, the measurements of FRF s can become critical in terms of measurement time and accuracy within a vehicle development process, where test-vehicle availability and quick countermeasures need to be addressed. The direct approach in transfer function measurements; with excitation at the interface, is often the most trusted. But it is not always easy to access the interface and to apply accurate excitation at the interfaces. And, when a large number of interface locations and directions need to be covered the effort can be tremendous. Using the assumption of linearity of a passive system, the identification of vibro-acoustic transfer using the reciprocal approach had become more and more accepted because it can reduce the measurement time and overcome instrumentation problems at chosen interfaces. The reciprocity relation for vibro-acoustic FRF is derived from a description of the system as a two port.

TRANSFER PATH ANALYSIS AND SOURCE IDENTIFICATION 3875 e1 i1 SYSTEM i2 e2 Figure 1 : Basic two port representation on a system The ports can be structural or fluid, or even; electric, magnetic, etc. As long as the system is linear and passive the following general reciprocity relationship holds; e ( ) ' ' ' ' 1 i1 + e2 i2 = e1 i1 + e2 i2 Watt (2) e1, e2 : denote pressure in the air, or force for a structure, or voltage for an electrical port, etc. i1, i2 : denote volume velocity in the air, or velocity for a structure, or current for an electrical port, etc. : denotes direct excitation; the energy enters the system through port 1. * : denotes reciprocal excitation; the energy enters the system through port 2. The pair of e and i determine the power into the system through a port. From relationship (1) specific reciprocity relationships can de derived between specific quantifies like force, pressure, current, etc. (References 1, 2, 7) For a vibro- acoustic system one port is structural. We consider force excitation. The other port is acoustic, where we consider the blocked pressure response. This is the most common used characterization of vibro-acoustic sensitivity of vehicle bodies. The following reciprocity relationship is derived: P2 : pressure spectrum (N/m2) ( H PF 21 Q 2 : volume acceleration spectrum ( m3/s2) X 1 : acceleration spectrum (m/s2) F1 : force spectrum (N) HPF21 : vibro-acoustic transfer function ( m-2) = P F ' 2 ' ' 1 Q = 0 2 X&& Q 1 2 1 F = 0 2 ( m ) (3) 3 Direct-Reciprocal transfer sensitivity The sensitivity study is using the comparison between reciprocal FRF s and direct FRF s. Based on an experimental approach, the comparison over different boundary conditions is performed in order to quantify the influence of various parameters such as the alignment of accelerometers with the

structural excitation, the choice of the exciter for direct measurements and the position of target microphones with respect to the source position. Reciprocal measurements are carried out using the source (Figure 2) positioned at the driver s ears. Typical frequencies covered by such an excitation device run from 20 to 1000Hz. The structural response is measured on the vehicle body side at engine mounts as well as on the front right shock absorber, all in vertical direction. Figure 2 : Low frequency volume source in a vehicle (left), and integral shaker mounted on a vehicle (right) Structural excitation applied at 4 locations as defined as response points in reciprocal measurement is considered using a small self-aligning and self-suspending shaker with (LMS-Qsources integral shaker) as shown on Figure 2. 180 3876 PROCEEDINGS OF ISMA2010 INCLUDING USD2010 Typical results between reciprocal FRF s and direct FRFs show a good, but not a perfect, agreement, as can be seen in figure 3 and 4. In particular at medium frequencies (200-1000 Hz) there are some smaller deviations between the direct and the reciprocal measurements that we wished to understand better. Pa/N db 70 60 50 40 30 20 10 0-10 -20-180 FRF lvvs:ave4:s/egmt:frnt:+z FRF EGMT:FRNT:-Z/driv:frle:S (3) 20 30 40 50 60 7080 100 200 300 400 500 7001000 Hz Figure 3 : Direct Reciprocal FRF s comparison for excitation and response at the front right engine mount

Figure 4 : Direct Reciprocal FRF s comparison for excitation and response at the right shock tower 3.1 Vehicle non-linearity influence It is known that shock absorbers in wheel suspension systems can show significant non-linearity at low amplitudes due to friction. The different amplitude levels during direct and reciprocal testing throughout the vehicle may affect the agreement. To reduce this effect we introduced a continuous motion over the shock absorbers during both the direct and the reciprocal FRF measurements. In figure 5 it can be seen that this clearly improves the lower frequency agreement, but there is of no significant influence on the medium and higher frequencies. 60 Pa/N db 180 TRANSFER PATH ANALYSIS AND SOURCE IDENTIFICATION 3877 70 60 55 50 45 40 35 30 25 20 10-180 20 30 40 50 60 7080 100 200 300 400 500 7001000 Hz 50 40 60 50 40 (Pa/N) db 30 20 10 0-10 -20 180-180 20 30 40 50 60 70 80 100 200 300 400 500 600 800 Hz (Pa/N) db Figure 5 : Direct Reciprocal FRF s comparison for the shock tower, left without shock absorber motion, right with motion ( red curve reciprocal, blue and green curves direct) 30 20 10 0-10 -20 180-180 20 30 40 50 60 70 80 100 200 300 400 500 600 800 Hz 3.2 Exciter influence in direct measurements When comparing direct and reciprocal vibro-acoustic measurements, the quality of the direct measurement should also be considered. An impact measurement hammer is commonly used as an excitation device for NVH analysis purposes. But, the quality of hammer impact transfer function measurements depends on the instrument, on the operator and on the access to the measurement location. First a comparison is made with a small self-aligning and self-supporting shaker (Figure 6).

180 3878 PROCEEDINGS OF ISMA2010 INCLUDING USD2010 Figure 6 : Instrumented hammer (right) vs. integral shaker (left) used for the comparison The differences between hammer and shaker FRF, as the example shown in figure 7, can be significant. Even if the measurement person is trained, we have found that in most cases the measurements with the small shaker showed a better agreement with the reciprocal FRF. -30 (m/s 2 )/(m 3 /s 2 ) db -40-45 -50-55 -60-65 -70-80 -180 20 30 40 50 60 7080 100 200 300 400 500 7001000 Figure 7 : Direct Reciprocal FRF s comparison for excitation and response at the front shock tower. Hammer (blue) vs. Integral shaker (green) compared with reciprocal measurement Hz An addition test was performed where 10 experienced persons used a modal hammer to measure a structural FRF on a good accessible location on a complete vehicle. The curves in figure 8 show that the variation in the excitation can explain the 10 db variability at medium frequencies.

(m/s 2 )/N db TRANSFER PATH ANALYSIS AND SOURCE IDENTIFICATION 3879-15 -20-25 -30-35 -40-45 -50-55 -60-65 -70 180-180 20 30 40 50 60 70 80 100 200 300 400 500 600700 1000 Figure 8 : Reproducibility of structural FRF. Average FRF (blue) and minimum/maximum envelope (red) based on 10 persons Hz 3.3 Accelerometers alignment in reciprocal measurements In reciprocal measurements as well as in direct measurements, both the 3D sensor alignment and the hammer impact direction can have a relevant contribution in the error induced to the vibro-acoustic FRF. To illustrate the importance of misalignment errors, the sensor orientation is modified by changing its angle with respect to the vertical direction. In the pictures below on the left the acceleration sensor was positioned to align as well as possible with the direct FRF excitation. -30-35 -40 ( m/s 2)/(m 3 /s 2 ) db -45-50 -55-60 -65-70 -75-80 180-180 20 30 40 50 60 70 80 90 100 200 300 400 500 600 700 800 1000 Hz Figure 9 : Direct - Reciprocal FRF s comparison with the interface accelerometer angled 20 +-3 degrees The measurement data in figure 9 gives an example of the deviation between direct and reciprocal responses with a poorly aligned accelerometer at the interface. Deviations up to 15 db, and phase deviations up to 90 degrees in medium frequency are apparently possible with a 20 degrees misalignment. In practice an alignment of the placed accelerometer housing to within five degrees is achievable.

3880 PROCEEDINGS OF ISMA2010 INCLUDING USD2010 3.4 Target microphone position vs. source position in direct and reciprocal measurements When performing direct measurements from the interface to the interior, the source is in place on the driver seat. This improves comparabilit y between direct and reciprocal transfer functions. But, the placement of the source means that the normal ear microphone location is now covered by the structure of the source. The acoustic center of the sound source is inside the active area. The sound pressure response during the direct FRF measurements is therefore acquired using multiple microphones placed around the source, as shown on Figure 10. Figure 10 : Microphones layout near the ear location and around the source during direct excitation at the interface As the acoustic wavelength become smaller when the frequency increases, the agreement between direct and reciprocal FRF s becomes sensitive to the exact spatial positioning of the microphones. The individual microphone locations near the acoustic centre show different curves, especially at medium frequencies, as visible in figure 11. 70 70 60 60 50 50 40 40 (Pa/N) db(a) 30 20 (Pa/N) db(a) 30 20 10 10 0 0-10 -10-20 400 Hz 800-20 400 Hz 800 Figure 11 : Direct vibro-acoustic FRF at the 7 locations around the ear location/source and the reciprocal measurement (red), 400 to 800 Hz. An average of four microphones around the acoustic centre of the source has the best agreement with the direct measurements, and was therefore used in the figures 3 to 9. But, if a single microphone location is the only possibility, then 10 mm from the middle of the driver is the best location.

TRANSFER PATH ANALYSIS AND SOURCE IDENTIFICATION 3881 4 CAE based sensitivity Experimental validation usually required a lot of care in order to perform reciprocal sensitivity analysis using different types of acoustic exciters. The consideration of CAE modeling can be taken advantage of both for repeatability purposes and to study test setup not practical. Nevertheless, the need to validate results and conclusions from CAE analysis is important. Therefore sound pressure correlation is performed as an additional step. 4.1 CAE Model Boundary Elements radiation Models (BEM) are considered for three different configuration in order to study the free field radiation for low and mid frequency {100Hz to 1200Hz} A detailed BEM model of the LMS Qsources low Frequency volume source is considered in the first case as shown on Figure12. The body of the source is discretized in with average 2D elements which size allowing analysis up to more than 3000Hz using the standard criteria stating that at least 6 FE elements should characterize one acoustic wavelength at the maximum frequency value. To represent the source driver, two excitation surfaces are defined based on their physical radiation properties: the main piston membrane in the central area and the surrounding area which defines the transition between the main piston and the rigid body. Both areas are assigned different velocity boundary conditions depending on their normal vibration properties Figure 11 : BEM Mesh of the source, left, and BEM Mesh of the Human Torso (mid). Active acoustic source assigned to few elements of the left inner ear (right) A detailed BEM model of a common human torso simulator is considered in the second case. The human torso is also meshed with element size valid up to 3000 Hz. The active area model at the entrance of the inner ear is represented a small area on the pinnacle having an equivalent source strength as the source applied to limited elements as shown on Figure 12 on the right. An ideal monopole acoustic point source is considered in the third case as the reference. This corresponds to a pulsating sphere radiating uniformly in all directions. The monopole is characterized by its volume acceleration Q, having its amplitude consistent between the source and the torso exciters. 4.2 Correlation with measurements In order to use the BEM acoustic analysis as an additional tool to compare and understand the acoustic field radiated by different acoustic exciters/receivers such as the source, a binaural torso and a monopole source/microphone, the correlation with some measurements is required.

3882 PROCEEDINGS OF ISMA2010 INCLUDING USD2010 Validation between experiments and CAE analysis is done for the acoustic source. The source was placed in a semi-free field environment. The radiation is monitored by 8 microphones placed at 360 on a horizontal plane from the source acoustic center. The source surface is standing above the reflecting ground as shown in Figure 13. The agreement of the measurement in semi-free field with the BEM model was good without any optimization on the model. The experiment confirmed that the BEM model can predict with a good accuracy the acoustic response in terms of directivity and pressure levels around the source body. Figure 12 : TEST (black) and CAE (red) acoustic transfer function Transfer amplitude in db and Phase 4.3 Dummy influence in reciprocal measurements When using reciprocal measurements by using the LMS-Qsources source, the reflecting body of the source aims at accounting for the human body. Above a given frequency which depends on the acoustic wavelength and the propagation medium, the acoustic near field is modified by the presence of the source and the vibro-acoustic transfer between the source and an accelerometer will therefore include this diffraction influence of the body of the source or torso. By comparing the acoustic radiation in the surrounding space of the three types of acoustic sources/receivers, the deviation between monopole, low frequency volume source and binaural torso is studied up to 1200Hz. The Indirect BEM/IBEM method is used to calculate the 3D acoustic radiation due to a given source strength. At a given frequency, the pressure is monitored up to 1m away from the estimated excitation center on a horizontal and a vertical plane having their origin coinciding with the estimated acoustic source center as shown on Figure 14. The acoustic source center is aligned between all exciters.

TRANSFER PATH ANALYSIS AND SOURCE IDENTIFICATION 3883 Figure 13 : Pressure evaluation horizontal and vertical planes for the low freque ncy source (left), the binaural torso (middle) and the monopole source (right) The comparison of the monopole source response with respect to the low frequency source response gives an insight about radiation and diffraction differences At 100Hz, the effect of the source and binaural torso body diffraction and source directivity were expected to be negligible, which was confirmed on Figure 15. The differences in the computed sound field mostly remain well below 1 db, as shown in figure 16. Figure 14 : Pressure distribution in vertical plane at 100Hz. Fixed scale 90 to 130dB Figure 15 : Pressure difference map between the monopole source and the LFVVS source at 100Hz. Fixed scale 0 to 20dB At 400Hz, the monopole radiation has already become different from the low frequency source and the binaural torso source due to the body diffraction effect. (Figure 17) But in the horizontal plane the difference due to the source directivity is still limited.

3884 PROCEEDINGS OF ISMA2010 INCLUDING USD2010 Figure 16 : Pressure distribution in vertical plane at 400Hz. Fixed scale 90 to 130dB The pressure difference in the horizontal plane is symmetrical and more important in the semi space located in the front of the source direct radiation space. The pressure difference in the vertical plane is asymmetric and more pronounced in the quarter of space in line with the piston surface directivity. At 800Hz, the monopole radiation has become very different from the low frequency source and binaural torso. The body diffraction and directivity effects are significant. The low frequency source responses also starts to deviate slightly from the binaural torso response in the direct radiation field and behind the source as shown on Figure 18 and 19. Figure 17 : Pressure distribution in vertical plane at 800Hz. Fixed scale 90 to 130dB Figure 18 : Pressure distribution in vertical plane at 800Hz. Fixed scale 90 to 130dB The simulation at 1000 Hz shows even clearer the influence of the source or torso on the sound field. (Figure 19) The differences between the torso and the low frequency volume source also increase, with +- 8 db effects in amplitude which seem to spread over various angles. (Figure 20)

TRANSFER PATH ANALYSIS AND SOURCE IDENTIFICATION 3885 Figure 19 : Pressure distribution in vertical plane at 1000Hz. Fixed scale 90 to 130dB Figure 20 : Pressure difference map between the torso and the source at 1000Hz. Fixed scale 0 to 20dB The simulation also shows that the diffraction differences between the low frequency volume source and a torso increase with frequency. This may affect the validity of vibro-acoustic transfer functions at higher frequencies in relation to the sound pressure as perceived by a human. The simulation results indicate that the differences increase strongly above 1000 Hz, as shown at 1200 Hz below in figure 21. Figure 21 : Pressure distribution in vertical plane at 1200Hz. Fixed scale 90 to 130dB

3886 PROCEEDINGS OF ISMA2010 INCLUDING USD2010 5 Conclusions A good agreement between direct and reciprocal measurements on complete vehicle over the 20 to 1000 Hz frequency band is well possible. But the agreement is usually not perfect and it can be disappointing too. The reasons are now more clearly understood. The effects to take into account when verifying vibro-acoustic reciprocity: - the force excitation and the accelerometer response alignment is critical - the volume source should be present both during direct and reciprocal measurements - the location of the response microphones near the ear location is critical, and spatial averaging is advised - non-linearity can influence the results on complete vehicles, especially at frequencies below 50 Hz. - it is better to use a well aligned shaker instead of hammer impact measurements which are more difficult to reproduce. The simulation results show that, the difference between either a torso or the low frequency sound source and a perfect point source or point receiver is already signif icant from 200 Hz upwards. So even below 1000 Hz the diffraction of a human body has a significant effect. The simulation also showed that the differences in radiation between the LMS-Qsources low frequency volume source and a torso increase with frequency, with large differences above 1000 Hz.