Binaural Transfer Path Analysis and Synthesis (BTPA BTPS) using Substructuring Techniques Based_图文

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SAE TECHNICAL PAPER SERIES

2007-01-2226

Binaural Transfer Path Analysis and Synthesis (BTPA/BTPS) using Substructuring Techniques Based on Finite Element Analysis (FEA) and Measurements
R. Sottek and B. Müller-Held
HEAD acoustics GmbH

Noise and Vibration Conference and Exhibition St. Charles, Illinois May 15-17, 2007
400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-0790 Web: www.sae.org

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2007-01-2226

Binaural Transfer Path Analysis and Synthesis (BTPA/BTPS) using Substructuring Techniques Based on Finite Element Analysis (FEA) and Measurements
R. Sottek and B. Müller-Held
HEAD acoustics GmbH
Copyright ? 2007 SAE International

ABSTRACT
Binaural Transfer Path Analysis and Synthesis (BTPA/BTPS) were originally developed for assessing the binaural contributions of individual vehicle noise paths. They are powerful modeling tools, enabling engineers to explore noise transfer mechanisms by distinguishing between excitation source strengths and the transfer behavior of individual elements. The methods used in BTPA and BTPS are now more frequently confronted with limitations which can only be handled by detailed observation of the various influencing variables. A promising method is to describe the mechanical interfaces via four-pole parameters. Using this technique, changes in transfer paths (e.g. exchange of engine mounts) can be simulated by a tool providing immediately-audible results.

possibilities by virtually changing the geometry (e.g. shape, wall thicknesses…) and/or material properties. The effects of the modifications on the vehicle interior sound can be analyzed and subjectively evaluated during listening tests even in the early design phase. For demonstration purposes, the described method is applied to a small vehicle simulator with reduced complexity. This model allows for fast structural changes, and its operation is also very flexible with respect to source strength modifications. The results of the measurements and simulations will be presented.

VEHICLE SIMULATOR FOR BTPA DEMONSTRATION
cabin shaker

INTRODUCTION
The methods of BTPA/BTPS have been developed and refined during the past decade. They have successfully been used for troubleshooting and sound design of engine-related vehicle interior noise. These tools enable exploring the causative mechanisms for noise transfers, based on measurements of excitation source strengths and the corresponding structure-borne and airborne transfer paths to a receiver position (e.g. the driver position). The engineer can analyze and listen not only to the overall sound comparable to a binaural recording of the vehicle interior sound, but also to components of the total noise transmitted via a single path or a combination of paths to identify the cause of a particular disturbing noise pattern [1]. The next step in a sound design process includes modifying noise and vibration sources and/or transfer paths. This paper will introduce a new extended BTPS approach allowing the engineer to predict the impact of particular structure-borne transfer paths with the help of four-pole parameters [2], [3] calculated by Finite Element Analysis (FEA). The simulated transfer paths can be substituted for the original measured paths in the BTPSmodel. This approach offers new sound design

microphone

engine mount z body y x

engine mount

loudspeaker

Fig. 1: Vehicle simulator In Fig. 1 a small vehicle simulator is shown. A chassis is placed with three mounts on a soft, damped base plate to prevent external disturbances. On one side a cabin with Plexiglas is attached. Inside the cabin is a microphone, representing the driver’s ear. On the other side of the chassis are two sources which together represent an engine. A shaker mainly produces structure-borne noise. It is fixed to a beam which is screwed with two thin engine mounts to the chassis. A loudspeaker is integrated into the model to produce mainly airborne noise. This vehicle simulator has accordance to a real vehicle, in the sense that a cabin is

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coupled over a chassis and different engine mounts to the engine. Also the airborne transfer path of the engine is taken into account.

BINAURAL TRANSFER PATH SYNTHESIS The calculated transfer paths will be used as filters that place any chosen value of the engine-side acceleration in relation to the output signal, the sound pressure which can be measured at the driver’s ear. Therefore an input measurement has to be made to define the value of the above-mentioned acceleration. Under running engine conditions the acceleration before each engine mount and the sound pressure at all different airborne excitation sources are measured as input, and the binaural sound pressure of an artificial head at the driver position inside the cabin as output. In the case of the vehicle simulator, the acceleration before each mount and the sound pressure in front of the loudspeaker is measured as well as inside the cabin. For those measurements a real engine run up-recording is used as input signal. An engine airborne sound is played via the loudspeaker and an engine acceleration signal via the shaker. The measured input acceleration before the engine mount is convolved with the three transfer functions for each direction in space and each mount to get the synthesized structure-borne part of the noise at the driver’s position. All these transfer paths can be summarized into one structure-borne path (Fig. 2).

INTRODUCTION INTO BTPA/BTPS
The challenge of the BTPA/BTPS method is to break down a complex noise into its components. Therefore all acoustically-relevant sources must be detected and taken into account in the BTPA/BTPS model. These sources are divided into the structure-borne and airborne paths which will be introduced in the next paragraphs. STRUCTURE-BORNE TRANSFER PATH Each structure-borne transfer path from the engine to the driver’s head can be described using three transfer functions, one after another: the mount transfer, the apparent mass and the acoustical transfer function. The mount transfer function abody/aengine can be determined in real cars under running engine conditions. In the example of the vehicle simulator the acceleration at both terminals of the engine mount is measured with shaker excitation using a sweep signal or with impact measurements at the engine side of the mount. The apparent mass, which is the ratio of the force to the acceleration at the body-side Fbody/abody, and the acoustical transfer function, which is the ratio of the sound pressure level at the driver’s head to the force at the body side pdriver/Fbody, will be simultaneously measured by body-side impact hammer measurements. Alternatively, the acoustical transfer function can be determined by reciprocal measurements [4]. In the case of the vehicle simulator the sound pressure in the cabin will be measured monaurally with one reference microphone. These measurements must be repeated for each mount in all three directions in space. AIRBORNE TRANSFER PATH The airborne transfer functions can be defined as pdriver/pengine for each possible sound source. In real cars, these sources can be at different positions in the engine compartment, at the intake system and at the exhaust pipe. To determine these transfer functions the sound pressure is measured at both ears of an artificial head placed on the driver’s seat while exciting with a loudspeaker in the vicinity of the assumed sources. Another approach is based on reciprocity [4]. In the case of the vehicle simulator the sound pressure is measured with two microphones, one in front of the loudspeaker and one inside the cabin. A sweep signal is played via the loudspeaker in order to measure the airborne transfer function.

input measurement

aengine x

abody Fbody pdriver aengine abody Fbody

synthesized structureborne sound

pdriver

mount transfer impact measurement measurement
Fig. 2: Structure-borne transfer path To calculate the synthesized airborne sound contribution at the driver’s position the sound pressure in front of the loudspeaker can be convolved with the separatelymeasured transfer function pdriver/pengine.
airborne transfer path
pengine
pdriver p engine

airborne a

p

driver

structure-borne transfer path, e.g. for one engine mount
mount transfer apparent mass
Fbody , X abody , X

acoustical transfer
pdriver , X Fbody , X

?p
pdriver , X pdriver ,Y

driver

aengine, X aengine,Y aengine,Z

abody , X
aengine, X

abody , X abody ,Y abody ,Z

Fbody , X Fbody ,Y Fbody ,Z

abody ,Y aengine,Y

Fbody ,Y abody ,Y Fbody ,Z abody ,Z

pdriver ,Y Fbody ,Y pdriver ,Z Fbody ,Z

structure-borne

abody ,Z aengine,Z

?p
pdriver ,Z

s

driver

Fig. 3: BTPA/BTPS model with one airborne and the structure-borne transfer paths for one mount.

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By summing both the structure-borne and airborne contributions, the total sound pressure at the driver’s position can be synthesized (Fig. 3). Due to the fact that the sound pressure at the driver’s position is measured in the input measurement as well, the synthesized sound pressure can directly be compared with the measured reference signal. Fig. 4 shows both measurements without any compensations or corrections of the transfer functions.
f/Hz 2k f/Hz 2k

Z Sha ker

shaker Z Sha ker
F shaker
Z
v sha ker

Z

mount l

mount r

F1r

v1r

F1l
mount r

v1l

mount
F2 r

Z
v2 r

mount
F2 l
v2 l

Z

mount l

Fbody

vbody

Z body r
1k 1k

Z body l

body

Z body

500

500

Fig. 5: Modeling the vehicle simulator using four-poles Fig. 5 shows how the vehicle simulator can be divided into four-pole parameters. Each mount can be described as a four-pole connected to a source (shaker) and a load impedance (body). TEST-RIG MEASUREMENTS All four-pole parameters of the mounts can be determined using a test rig. Therefore the mounts are clamped, dependent on the shape of the mount, with one single input and output between a dynamometer and an excitation source, a shaker. Additionally, a static preload can be applied to the mount. As an input signal a sweep for the frequency range of interest is used. The acceleration/velocity and force at both terminals of the mount can be measured. To calculate all four-pole parameters with the system of equations
§ F1 · ¨ ? ¨F ? ? 2? § Z 11 Z 12 ·§ v 1 · ¨ ?¨ ? ¨Z ?¨ ? ? 21 Z 22 ?? v 2 ?

200

200

synthesized signal Simulation synthesized signal
5 10 20 10 30 15 t/s 20 40 L/dB[SPL] 25 70 30 80

100

reference signal reference signal
5 10 20 10 30 15 t/s 20 40 L/dB[SPL] 25 70 30 80

100

50 35 90 35 90

50

Fig. 4: Comparison of the measured reference signal with the synthesized signal at the driver’s position inside the cabin The described BTPA/BTPS technology has become well-known over the last decades. The challenge is the correct adaptation of each transfer function concerning effects like crosstalk, etc.

SUB-STRUCTURING TECHNIQUES FOR THE BTPA/BTPS
An especially important methodology improvement for structure-borne transfer paths is to describe the mechanical interfaces via complex four-pole parameters. The goal of these efforts is to divide each transfer path into partial structures taking into account the coupling between the subsystems. Each subsystem, which can be considered a point-to-point connection (single input – single output) can be modeled by input, transfer and output impedances. This requirement is fulfilled for most engine mounts. If one component is modified, the simulation only needs to be performed for the modified substructure rather than for the entire transfer path [3]. This method allows the use of engine test-rig measurements or FEA simulations for simulating structure-borne contributions in cars without installing the separately-measured or simulated parts, like mounts, in the car, taking into account the different impedances of body and test rig. The description of a component using four-pole parameters is independent of the load. Knowing the impedances of the car at the engine mount positions (engine and body side) and the four-pole parameters of the engine mount, a complete simulation of the signal transmission from engine to body and finally to the driver’s ears can be carried out. Any combination of test-rig, FEA- and vehicle data is possible.

(1)

two operating conditions are necessary to determine all four variables Z11, Z12, Z21 and Z22. In the case of test-rig measurements, it is possible to measure the mount upside-down to achieve these two conditions. FEA CALCULATIONS To calculate the four-pole parameters of rubber mounts with the help of FEA several requirements must be considered. In a first assumption the material of rubber can be approximated to be linear-elastic in the low frequency range up to 500 Hz. With this assumption the material data like the Young’s-modulus, the density and the Poisson’s ratio must be determined. Calculation of Young’s modulus With a linear elastic approach the Young’s modulus of the rubber mount can be determined by the deflection at a given maximum pressure delivered by the manufacturer. It is very important when modeling, that the geometrical boundary conditions like the connection threads or thread holes are made carefully and the weight of the model corresponds to the actual weight. By creating an assembly with three parts, head clamping

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plate, rubber mount, and the base plate, one can take into account the different materials rubber and steel. With this method a good approximation can be achieved which later can be adapted to the real measurements. Calculation of four-pole parameters with FEA The four-pole parameters of a mount are calculated with the FEA method: To determine the force and deformation/velocity at both terminals of the mount, reference nodes must be created. These reference nodes are connected to all nodes that touch the interface between mount and body, with rigid weightless elements. The clamping of the reference node at the body side is ideally stiff (infinite mechanical impedance). An additional adapting mass is generated at the reference node at the engine side. A standardized input load of 1 N is placed at this reference node (Fig. 6).
F
head clamping plate

additional masses like screw nuts, clamping parts etc. or by an inaccurate Young’s modulus value.
60 impedance Z11 dB [Ns/m] 50 40 30 20 10 impedance Z12 dB [Ns/m] 60 50 40 30 20 10

test-rig test rig measurement FEA simulation FEA simulation 200 400 600 800 frequency f [Hz] 1000

test-rig test rig measurement measurment FEA FEA simulation simulation 200 400 600 800 frequency f [Hz] 1000

Fig. 7: Comparison of the four-pole parameters Z11 and Z12 based on test-rig measurements and FEA calculations A fitting algorithm allows for adapting the Young’s modulus, the damping coefficient and the additional mass. As a result the adapted FEA-calculated four-pole parameters are given. Fig. 7 shows the comparison between the results achieved with test-rig measurements and with FEA simulations. Calculation of four-pole parameters without adaptation Based on the adapted FEA calculation in z-direction all parameters and boundary conditions of the FEA-model are corrected. Just by changing the direction of the input load, the reaction forces and deformations affected by this new boundary condition can be recalculated. Due to the symmetry of the mount the input and output impedances of the x- and y-direction are the same and therefore also each corresponding four-pole parameter.

input load 1N surface is connected with the input load additional mass for mass compensation of screws

rubber mount

fixturing to ground
base plate

harmonic response analysis: .. . ~

m x  d x  kx
Fig. 6: FEA simulation

F

By means of a harmonic response analysis the reaction forces FR = -F2 at the clamped node and the deformation x1 at the input node can be calculated in the frequency domain, likewise the reaction moments and the twist angles at the input in all directions in space. Due to the defined boundary conditions, the input force is identical to the input load of 1 N. Of course there is no deformation at the clamped node due to the fact that this node is rigid. The four-pole parameters Z11 and Z12 can be calculated as (f: frequency)
Z 11 F1 v1 1 v1 1 x 1 j 2Sf Z 12 F2 v1 F2 x 1 j 2Sf

INTEGRATION OF THE FOUR-POLE PARAMETERS INTO THE BTPS MODEL
CHARACTERIZING THE TRANSFER IMPEDANCE UNDER FINITE LOAD CONDITION Up to this point it has been described how the transfer functions work against infinite rigid impedances like a mount attached to the ground. On the other hand, if the mount is coupled to any kind of load impedance this impedance must be known and taken into account for the calculation. For example in a car the load impedance Zbody can be determined by performing an impact hammer measurement at the body side of the engine mount. All necessary load impedances can be determined, measuring in all three directions in space. The values achieved from the load impedance Zbody measurements can now be combined with the calculated four-pole parameters from the FEA simulation and the test-rig results to calculate the transfer function

(2)

By turning the mount upside-down and exchanging the clamped node and the load input node, the parameters Z22 and Z21 can be calculated. The transfer impedances Z21 and Z12 are identical for reciprocal systems. In the vehicle simulator both mounts are symmetrical in the xy-plane which allows calculating the four-pole parameters in just one measurement (Z11 = Z22). Adapting FEA calculations based on test-rig measurements Due to some smaller FE-modelling errors there are some small variations between the FEA and test-rig measurements. These errors are caused by missing

F2 v1

Z 21 . Z 1  22 Z body

(3)

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L/dB[N/(m/s)] 70 60

obtained from two different approaches: first using testrig measurements and second using FEA simulations. Both results are shown together with results from impact measurements at the vehicle simulator. DESCRIPTION OF THE SOURCE

50 40 TF with Zbody TF without Zbody 50 60 80 100 120 160 f/Hz 300 400 500 600 1000

30 20

Fig. 8: Transfer impedance with and without considering the load impedance Zbody The need of considering the load impedance in the calculation is shown in Fig. 8. The transfer impedance from equation (3) is compared to the mount transfer function Z12. With the transfer function calculated in equation (3), the mount transfer function abody/aengine and the apparent mass Fbody/abody can be replaced in our synthesis for the structure-borne transfer path. Due to these sub-structuring techniques it is possible to combine test-rig measurements, FEA simulations and impact measurements in the car to calculate the structure-borne path from the engine to the driver’s ear inside the cabin (Fig. 9).

The procedure described above has shown how to calculate virtually the four-pole parameters of an existing engine mount, with test-rig or with FEA measurements. The main advantage is the virtual exchange of different mounts, without having to do any installations in the car. To be able to do this, one further aspect must be taken into account. The characteristics of the excitation source are affected by the engine-mount-chassis fixture or the engine impedance. If an engine is fixed to an infinite mass (without damping elements), there will be no acceleration but a large dynamic reaction force. Otherwise, if an engine is mounted to an infinite soft mount there are nearly no dynamic forces but high accelerations. Due to this fact it is important to know the impedance and the source strength of the engine in order to characterize the whole system.

source dependent calculation

synthesized structure-borne sound

input measurement

synthesized structure-borne sound

aengine

Fbody pdriver x aengine Fbody
FEA, test-rig impact and impact measurement measurement

pdriver

aengine

Fbody pdriver x aengine Fbody
FEA, test-rig impact and impact measurement measurement

pdriver

Fig. 11: Structure-borne transfer path using predicted excitation signals based on engine accelerations on a test rig and four-pole parameters (FEA or test-rig measurements) as well as impact measurements (to determine load and source impedance) By integrating the source characterization into the BTPA/BTPS model it is possible to create a synthesized sound at the driver’s position without having an input measurement of the real car. Only engine test-rig measurements are needed. The engine acceleration can be predicted based on the engine source characteristics, the calculated four-pole parameters and the body impedance (Fig. 11). The source characterization is the subject of current research and has been shown to be very promising.

Fig. 9: Structure-borne transfer path with combined FEA and test-rig measurements
L/dB[Ns/m] 30

10 0 -10 -20 -30

test-rig measurement test rig measurement simulation using FEA FEA simulation vehicle simulator measurement vehicle simulator measurement
20 50 100 f/Hz 200 500 1000

-40 -50

VALIDATION
The use of a sub-structuring technique based on fourpole parameters (from FEA simulations or test-rig measurements) for the BTPA/BTPS model has been described above. This method is an extension to the standard BTPA/BTPS methodology which allows integrating virtual modifications to an existing BTPS model.

Fig. 10: Transfer impedance Fbody/vengine obtained using test-rig measurements, FEA simulations and vehicle simulator measurements Fig. 10 shows the transfer impedance calculated with equation (3). The four-pole parameter Z22 and Z21 are

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With the help of the vehicle simulator many calculations, FEA simulations and combinations of both, have been examined. The main focus was to describe different structure-borne transfer paths by using four-pole parameters. The four-pole parameters were determined for each engine mount in z-direction on a test rig. These measurements can also be done by FEA simulations, which then, however, must be adapted to the test-rig measurements (Fig. 7). With an adapted FEA model it is easy to obtain all moments and forces in all directions in space without time-consuming measurements.
f/Hz 500 f/Hz 500 f/Hz 500

Simulation modell ls+ks ( 0.00-43.69 s).FFT (4096,50.0%,HAN).

L/dB[SPL] 80 60 50 40 30 20 10

reference Referencemeasurement Signal Simulation using FEA simulation
50 100 200 f/Hz 500 1000 2000

0

300 240

300 240

300 240

Fig. 13: Spectra of the measured reference signal and a synthesis achieved by FEA-calculations, considering both structure-borne and airborne contributions.

CONCLUSION
160 160 160 120 120 120

80

80 Reference reference reference measurement measurement 5 30 40 10 15 t/s 20 L/dB[SPL] 25 30 70 modell synthesis synthesis with vehicle simulator (measurements) measurement 5 30 40 10 15 t/s 20 L/dB[SPL] 25 30 70

80

synthesis synthesis with integrated FEA based on FEA simulations
5 30 40 10 15 t/s 20 L/dB[SPL] 25 30 70

60

60

60

It has been shown that the traditional BTPA/BTPS methodology can be extended using four-pole parameters not only from test-rig measurements but also from FEA simulations. Via this method it is possible to design or to modify existing parts such as mounts with respect to acoustics. For the prediction of the effects due to structural modifications, an adequate source characterization is needed. The characterization of the structure-borne source is a part of recent research work, whose results will be published in the near future.

35 80

35 80

35 80

Fig. 12: Spectrograms of the total structure-borne noise based on FEA simulations (left) and vehicle simulator measurements (right) compared to the reference signal (centre). Fig. 12 represents spectrograms of the structure-borne noise, based on three different methods. On the left side, one can see the synthesis determined via the FEAcalculations and the input impedance of the body together with the acoustical transfer function, as described in Fig. 9. On the right side, the synthesis is exclusively calculated with data obtained from impact measurements at the vehicle simulator. This represents the established BTPA/BTPS method, as described in Fig. 2, with no virtual elements. Both syntheses add all the contributions of the transfer paths, calculated for both mounts of the vehicle simulator in all three directions in space. These two above-described syntheses are compared to the measurement in the cabin with the reference microphone (centre of Fig. 12). When examining the results of the syntheses one can detect some visible and also audible deviations from the reference, which however are small enough to be neglected. Finally, a BTPA/BTPS model was created, not only with the structure-borne transfer paths (both engine mounts in three directions in space) but also with the airborne transfer path. The synthesized structure-borne transfer paths were created by using sub-structuring techniques based on FEA four-pole calculations. The result is illustrated in Fig. 13.

ACKNOWLEDGMENT
This research work, especially with respect to the measurements and analyses on the vehicle simulator, has been supported by Maria Starnberg, a Swedish ERASMUS student from the RWTH Aachen University.

REFERENCES
1. Genuit, K. and Bray, W.: A Virtual Car: Prediction of Sound and Vibration in an Interactive Simulation Environment, 2001 SAE Noise & Vibration Conference Proceedings, Traverse City. 2. Sottek, R.; Riemann, D. and Sellerbeck, P.: Virtual Binaural Auralisation of Vehicle Interior Sounds, Proceedings of the Joint Congress CFA/DAGA’04, Strasbourg 2004. 3. Sottek, R.; Genuit, K., Behler, G. and Vorl?nder, M.: Description of broadband structure-borne and airborne noise transmission from powertrain, Proceedings of the FISITA 2006, Yokohama, 2006. 4. Sottek, R.; Sellerbeck, P. and Klemenz, M.: An Artificial Head which Speaks from its Ears: Investigations on Reciprocal Transfer Path Analysis in Vehicles, Using a Binaural Sound Source, 2003 SAE Noise & Vibration Conference Proceedings, Traverse City.


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