Prediction of Light Rail Vehicle Noise in Running Condition using SEA

Prediction of Light Rail Vehicle Noise in Running Condition using SEA Sebastian PREIS ; Gérard BORELLO Siemens AG Austria Urban Transport, Austria InterAC, France ABSTRACT A complete Light Rail vehicle was modeled with Statistical Energy Analysis (SEA) to investigate the airborne and structure-borne noise inside the cabin in running condition. To identify the complex dynamic behavior of the Body-In-White (BIW) a Finite Element (FE) model was converted into an SEA model and a Virtual SEA (VSEA) method up to 000 Hz was applied. In parallel an Experimental SEA (ESEA) test was performed on the BIW to identify the damping loss factors (DLF) and to generate coupling loss factor (CLF) and input mobility parameters in order to validate the VSEA model. Above 000 Hz and for the acoustic trim the VSEA model was extended using the Analytical SEA (ASEA) method. The final model, which was a combined VSEA/ASEA model from 00 Hz to 5000 Hz, was validated with measurement data. The input data for the model were the averaged sound pressure level in the area of the bogie and the localized constrained accelerations. The difference between the predicted and the measured sound pressure level was less than db. Keywords: Computational engineering, Experimental SEA, ESEA, Railway Noise, Statistical Energy Analysis, SEA, SEA+, Virtual SEA, VSEA, I-INCE Classification of Subjects Number(s): 3.4., 75.. INTRODUCTION To calculate the vibrational and acoustical behavior of a Light Rail Vehicle in a frequency range from 00 Hz to 5000 Hz in running condition it is still not possible to use only one simulation or measurement approach. To handle all sources and transfer paths it is necessary to use measurement data and different simulation approaches. This paper shows a possible way to combine SEA with Finite Element Method (FEM) and measurements. The final model is an SEA model where, in addition to the analytical SEA parameters, translated FE and measurement data are used as SEA parameters. With this combined calculation strategy one advantage of SEA is the capacity to integrate data from other approaches.. MODELING METHODOLOGY. FE modes are used to build a structural SEA model of a car body The metallic structure of a Light Rail Vehicle is complex (corrugated sheets etc.) and in the low and mid frequency range an analytical SEA model cannot provide modal densities and coupling loss factors (CLF) spectra with sufficient accuracy which are required by the SEA modeling process. Therefore a FE model of the BIW with a mesh which is useable up to 000 Hz transition frequency ( f t ) is processed with VSEA technique available in SEA+ software package. This model is then complemented with standard analytical SEA subsystems (for interior fluid volume and acoustic trims). VSEA is derived from experimental SEA analysis (, 4). Real modes are extracted using the Finite sebastian.preis@siemens.com gerard.borello@interac.fr 6660

Element Software Abaqus. Eigenfrequencies and related modal amplitudes, at a set of restitution nodes, are stored and exported to SEA+ VSEA solver. VSEA is synthesizing complex velocity Frequency Response Function FRF v i /f j = v ij at all restitution points M i in global x, y, z directions due to rain-on-the-roof unitary x, y, z forces applied at each restitution node M j. Finally the FE statistical information is given by the transfer velocity matrix V made of v ij elements. The assumed global damping loss factor for modal synthesis is taken equal to some default value for all modes. V matrix is compressed into /3 rd octave band and projected in the direction n i and n j of maximal input/output conductances given for at all nodes by Y =Re{Diag(V)}n. The final matrix V for SEA-parameter identification is then expressed in band-averaged format at center radial frequency and bandwidth B with elements given by c v (, B ) v ( ) d. () ij c ij B B V is finally auto-partitioned by SEA+ peripheral algorithm which groups nodes into a set of weakly coupled subsystems k leading to SEA rectangular transfer matrix are given by V of which elements v v kk ' i kk ' ij Nk jk. () SEA parameter identification is performed by solving the SEA inverse problem relating SEA loss matrix L through the normalized SEA power balanced equations. V to * IY / c Lm V L m V I Y / c (3) m is the subsystem mass vector and * indicates the pseudo-inverse. In practice with m N /4Y (4) the previous equation is reshaped for direct solve of modal density vector N. It leads to the local modal energy matrix power balanced equations given by with elements of ε given by I/ LNεL ε (5) and e kk ' i N v kk ' ij 4y y k jk i j (6) L= N N.. N....... NN.. NNN k' NNk ' k ' k ' k ' N N k ' (7) 666

ε has dimension of modal energy and leads to accurate identification of L thanks to SEA+ algorithm that performs auto-partitioning into weakly coupled regions. In practice, with lossless junctions, the previous system is solved for identifying ifying separately modal T * density and coupling loss factors. Model quality is assessed by comparing V 4Y L Y / with direct V FRF input. The Difference V V gives the reconstruction error matrix plot as reconstruction performance index in SEA+ (3). The Multi Scale-VSEA (MS-VSEA) patch method is a variant formulation of the inverse SEA problem where the auto-partition is applied to pre-defined group of nodes instead of all FE nodes. This method is thus providing a partition per frequency band corresponding to a specific grouping of patches into subsystems. The main advantage is to accurately reconstruct FE transfers over the whole frequency range. Figure shows the flow chart of the VSEA process. Figure VSEA data flow. Analytical SEA prediction above FE frequency limit An SEA expander can be allocated to a VSEA subsystem. The expander is a classical SEA subsystem. Its parameters are derived from analytical theory in order to take over the calculation of SEA CLF and modal densities above the transition frequency f t. Patches may be conveniently chosen by the user for easier modeling of analytical SEA expanders by defining a patch as a group of FE with same section property for example. Above f t both junction CLF and subsystem modal densities are analytically expanded to high frequencies..3 VSEA and analytical fluid/structure coupling VSEA or MS-VSEA subsystems are coupled to analytical SEA cavities through a specific statistical radiation integral calculated by spatial windowing of an elementary infinite structural wave (6). The related structural VSEA wavenumber is estimated from ratio of rotational over translational nodal principal-direction conductances. For a subsystem of domain k, k Y Y R T k k (8) were Y R and Y T are maximal local rotational and translational conductances averaged over k, respectively. 666

.4 Adding acoustic trims to the bare structure All soft parts (internal trim panels, acoustic materials) are modeled as additional analytical subsystems or as attenuation spectra that filter the sound radiation. The latter are predicted by Transfer Matrix Method (TMM). Given an acoustic trim made of several layers (porous and/or elastic materials), related transmission (TL) and insertion (IL) losses are predicted by TMM under random incidence and infinite layer dimension. TL and IL are corrected for taking into account finite size of the trim. The base panels modeled as SEA subsystem are modified by trim presence (added mass and added damping)..5 Modeling indirect CLF Indirect CLF between acoustic cavities separated by intermediate thin panels are modeled by either mass law connection applied in parallel to the resonant radiated energy of the structural modes or by adding Black energy transfers to the SEA model (7). Black energy corresponds in SEA+ to the non-resonant energy driven by mass produced by interaction of White (resonant) energy of emitter subsystem to Black energy of the receiver subsystem. As Black energy is per definition non-dissipative, additional constraint equations are introduced to the SEA matrix for their prediction. Below f t, both structural direct and indirect CLF are identified by VSEA solver. Above, CLF of direct structural junctions are expanded by analytical modeling assuming infinite line or point junctions and applying spatial windowing for making finite-sized corrections when necessary. Nevertheless, no analytical theoretical model is currently available for predicting indirect structural CLF above f t. For high frequencies, indirect CLF are expected to progressively vanish and to converge to SEA asymptotic vibratory state driven by only direct CLF. They are then interpolated with some user-defined decreasing slope..6 Validating and measuring additional parameters Experimental SEA (ESEA) (4, 5) has been used for getting BIW DLF as well as some CLF for further validation. SEA-TEST is used for post-processing measured FRF under hammer impact. Bijection can be made between measured ESEA and VSEA subsystems, leading to better control on natural dispersion of calculation regarding actual dynamical behavior. Figure shows the interaction between data from test and FE calculation with SEA simulation. SEA+ model Loads ESEA TEST BIW FE VSEA Structure (MF) ASEA Cavity TMM Trim ASEA Expander (HF) OPERATING CONDITIONS Figure Logical diagram of an SEA+ model 6663

3. Modeling a Light Rail Vehicle 3. Model of BIW For model validation and for the SEA parameter DLF an ESEA measurement was performed on the car body. Complex driving point and transfer mobilities were measured on the Light Rail Vehicles structure. ESEA calculation was done with SEA-TEST software. In parallel for the VSEA model eigenfrequencies and modal amplitudes of the BIW were calculated with FEM and imported in the VSEA module of SEA+ (see Figure 3). Figure 3 Imported FE data are stored in nodes (red) in VSEA model As described in chapter VSEA algorithm calculates out of FEM global modes the transfer velocity matrix V. Then nodes are grouped into weakly coupled SEA subsystems and SEA parameters like modal density, CLFs and indirect CLFs are derived. For the model DLFs were used from ESEA measurement. Above the transition frequency f t analytical SEA subsystems were used. The final combined model of the BIW was a VSEA model from 00 Hz to 000 Hz and an analytical SEA model from 000 Hz to 5000 Hz (see Figure 4). Figure 4 Model of BIW with direct (red) and indirect (yellow) junctions 6664

Figure 5 shows a comparison of a measured and simulated average velocity response of a subsystem were a unit point force load was applied. Average Velocity 0 Simulation Measurement Average Velocity [m/s] 00 000 Frequ. [Hz] Figure 5 Comparison Average Velocity simulation with measurement (of a subsystem) 3. Model of a complete Light Rail Vehicle For the model of a complete Light Rail Vehicle the BIW was complemented with the acoustic trim. This was done as described in chapter with TMM or with further analytical SEA subsystems. Furthermore SEA cavities were connected inside and outside the car body to the structure (see Figure 6). The input data of the sources were measured in running condition on a test track. For the airborne source the average sound pressure level of 6 microphones in the area of the bogie and for the validation microphone in the cabin were measured. The averaged sound pressure level was the acoustic input of the cavity below the rail car. The measured accelerations of the lower car body constrained the SEA subsystems in the floor area. Figure 6 Model of a complete Light Rail Vehicle 6665

3.3 Result The sound pressure level inside the cabin was calculated between 00 Hz and 5000 Hz. For validation the result was compared with measurement data which were measured up to 500 Hz (see Figure 7). The difference of the A-weighted overall sound pressure level from 00 Hz to 500 Hz was.3 db. 0 db(a) sound pressure inside rail car at specific speed simulation measurement SPL(A) [db] 00 000 0000 Frequ. [Hz] Figure 7 Comparison A-weighted sound pressure level 4. CONCLUSIONS A complete Light Rail Vehicle in running condition was modeled with SEA in the frequency range from 00 Hz to 5000 Hz. For higher accuracy in the low and mid frequency range VSEA, which derives the SEA parameters from FE data, was used. This paper shows that the combination of SEA, VSEA and SEA-TEST (derives SEA parameters from measured data) leads to a robust SEA model with a good performance over a wide frequency range. The difference between the measured and calculated result of the overall A-weighted sound pressure level was.3 db. Furthermore it shows that is not necessary to calculate the acoustic behavior of a Light Rail Vehicle in the frequency range below 00 Hz for example with a FE model because the A-weighted sound pressure level is dominated in the mid frequency range. One big advantage of an SEA model is to give the acoustic engineer insight into the acoustic behavior of a model. A reason for that is that SEA concentrates statistical physical parameters into subsystems which organizes a very complex problem into a understandable number of smaller tasks. This and the possibility to integrate data from both FE calculations and measurements leads also to the possibility to apply advanced acoustic simulation already in the early design phase where the final design of a product is not entirely defined. 6666

REFERENCES. G. Borello, L. Gagliardini, L. Houillon, L. Petrinelli, Virtual SEA-FEA-Based Modeling of Structure-Borne Noise, SVM, January 000. M. Villot, C. Guigou-Carter, L. Gagliardini, Predicting the acoustical behaviour of finite size multi-layered structures by applying spatial windowing on infinite structures, JSV, Volume 45, Number 3, August 00, pp. 433-455(3) 3. SEA+ User-Guide version from 04 (InterAC SARL) 4. N. Lalor, The Experimental Determination of Vibrational Energy Balance in Complex Structures, Paper 0849 Proc. SIRA Conference on Stress & Vibration, 989, London 5. SEA-TEST User-Guide version from 04 (InterAC SARL) 6. G. Borello, L. Gagliardini, D. Thenail, Virtual SEA for Noise Prediction and Structure Borne Sound Modeling, Rieter Automotive Conference, June 4-5, 007, Pfaffikon, Switzerland 7. G. Borello, Evolution des méthodes de calcul vibroacoustique des systèmes industriels en fonction de la fréquence, CFA, 4-5 Avril 06, Le Mans, France 6667