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INTER-NOISE 200728-31 AUGUST 2007ISTANBUL, TURKEY
Temporal prediction of acoustic pressure radiated by vibrating structures: Subjective evaluation
N. Hamzaouia , J.D. Chazotb , G. Guyaderc
a, b : Institut National des Sciences Appliquées de Lyon, Laboratoire Vibrations Acoustique Bâtiment St. Exupéry, 25 bis avenue Jean
Capelle, 69621 Villeurbanne Cedex, France c : Renault …………………………………………………..
ABSTRACTThe main objective of this paper is to predict acoustic pressure radiated by the vibrating structures, in the temporal field. It will enable us to carry out sound hearings and to analyze the subjective effects of some parametric variations on the sound quality of vibrating structures; it is thus necessary to have an enough fine temporal sampling to ensure this task. The solution of this problem in the frequency field is based on the resolution of the Kirchhoff integral equation, which is very greedy in computing time and is thus limited to low and intermediate frequency. Simplifications in the frequency field were already brought, in low frequencies (under flim1), and in high frequencies (above flim2), and lead to a fast and precise calculation of this integral. Apart from this simplification, one needs to calculate the parietal acoustic pressure of the vibrating structure, which requires the use of the boundary element method. In this paper, we suggest a simplification of this parietal pressure, characterized by limiting frequencies (Flim1 et Flim2) which depend on structure dimensions and its position compared to the observation point. To avoid complete calculation (BEM), we must choose a minimal distance to respect in order to have flim1=flim2. This approach is carried out in the temporal field, and must be applied to the radiation of a thermal engine, but is first applied to a parrallelepipedic box. Vibratory data are given by temporal measurements made on a steel box excited on one of its faces by two pots of mechanical excitation. Acoustic pressures calculated in the temporal are then confronted with measurements, by using subjective tests of similarity, integrating a variation of excitation parameters.
1 INTRODUCTION
Sound picture of industrial products becomes more and more important in communication and is commonly transcribed by sound logos (related either to a brand or a product) or functional sounds remembered by consumers. To start a sound design process, it is necessary to set the means to judge and evaluate sound perception. It is also necessary, for a specific product such as an internal combustion engine, to identify sources and their characteristics. Sound synthesis presented in this paper comes within this process, and is aimed to give a tool to assess sound quality of an engine, and to link technical solutions to emitted sound. The present work focuses on acoustic radiation of vibrating structures, modelled by Kirchhoff integral that is usually solved using numerical methods such as boundary element method
a Email address: [email protected] Email address: [email protected] Email address: [email protected]
(BEM). This kind of method, often applied in frequency domain, is still very time consuming due to mesh refinement with increasing frequency. In frequency domain, several researchers have contributed to calculus optimisation with different simplified approaches (equivalent sources, numerical optimisations of BEM, physical considerations,…). In the same way, we suggested [1] and [2] a simplification of BEM for low frequencies and high frequencies with a simple integral that gives a global quantitative satisfaction (good prediction of high sound levels for a parallelepipedic box excited by a punctual mechanical excitation), but is still limited by the size of the mesh at high frequency. Differences between measured and calculated spectrum can be related to parametric uncertainties due to the method employed (structural mesh density, estimate of normal to vibrating envelop, frequency step, …). Qualitative evaluation will then enable to organize into a hierarchy all the parameters according to their influence by comparing measured to calculated sounds with a subjective test.
Prediction of radiated sound in time domain is the tool to evaluate the influence of simplifications and parameters that take part in this approach. In this paper, a simplification of the prediction by integral equation is presented, and an perceptive evaluation is applied on predicted and measured sounds.
2 PROBLEM FORMULATION
A vibrating surface coupled to an external fluid volume is considered, and Sommerfeld conditions are assumed. Pressure radiated by the vibrating surface is given by following linear acoustic equations :
Sommerfeld conditions at infinity
(1)
Solution of this problem is given by integral equation (2) where acoustic pressure radiated at an observation point M of external volume V is obtained from parietal acoustic pressures and velocities of the vibrating surface and from a Green function and its derivate.
(2)
With t’= t- ; Green’s function and its normal derivate at each point M0 of the envelop are expressed by :
(3)
After a time integration, and a discretisation of the vibrating surface in N elementary surfaces, solution can be re-written with tri = t- ri/c :
(4)
Acoustic radiated pressure is calculated with Equation (4) from the calculation of acoustic parietal pressure and its derivate for each point M0 of the vibrating surface. In order to avoid a time consuming calculation, we suggest simplifications related to acoustic behaviour in low and high frequencies.
2.1 Low frequency simplification
At low frequency, acoustic wavelength is much greater than the largest size of the structure (>>L). The following assumption can therefore be made :
; and integral equation (4) becomes :
(5)
2.2 High frequency and far field simplification
For high frequency, and far field (k2r2>>1), one can consider that
(acoustic impedance of spherical wave).
Simplification of equation (4) leads then to the following simplified expression :
Mi
M
ri
nMi
i
(6)
2.3 Frequency limits of validity for the two formulations
The low frequency formulation given by equation (5) is valid for wavelengths such as >>L . In the frequency domain, this condition writes : f << c/L. Taking for example a length L=1m, and c=340m/s leads to a maximal limit frequency Flim1 of 340Hz.
Validity of the high frequency formulation in equation (6) is given by the following condition on wave numbers : k2r2>>1, that can be transcribed in the frequency domain by : f >> c/2r. Taking for example a distance r=0.5m, and c=340m/s leads to a minimal limit frequency Flim2 of 108Hz.
With a security factor of 10, limit frequencies for the two formulation with L=1m and r=0.5m change to Flim1=34 Hz and Flim2=1080Hz. Between these two frequencies, the complete formulation is necessary.
Limit frequency Flim1, determined by a characteristic size of the structure, is a constant but the minimal distance r will enable to match Flim2 to Flim1 and hence to avoid the use of the complete formulation (2).
3 EXPERIMENTAL COMPARISONS
3.1 Thermal engine application
The first try is an experimental bench with a thermal engine (see photo n°1). Time prediction of acoustic pressure with simplified formulations (5) and (6) is used with measured velocities (14 accelerometers located at different places on the engine). Geometrical complexity of the engine, and also the presence of secondary sound sources shows the importance of some parameters on the result quality such as the number and the place of accelerometers, or the distance between the engine and the observation point . For the engine, the number of points must not be too important, but the location is very important since it must take into account all the acoustic radiating sources. A filtering of other sound sources is necessary if one wants to compare synthesised results with measured data. The interest of the method is to be able to isolate in synthesised results the sound emitted by each source and then to evaluate their perception.
(5) (6)Formulation Complète (2)Flim1
frequencyFlim2
Photo n°1 : Engine bench (gear box side)
Listening of calculated and measured sound becomes similar when a frequency filtering is applied to eliminate sound sources not taken into account by vibratory measurements. Uncertainties on elementary surfaces associated to measurements points play an important part in quality of sound synthesis. Without measurements on cylinder head, synthesized sound is very far from a real engine sound, whereas taking or not measurements made on oil housing gives the same result.
Two tests on perception of sound similarity lead to conclusions and perspectives with this approach. The first one was between 12 calculated sounds and one measured sound. The 12 sounds were obtained with several changes in calculation parameters such as elementary surface, limit frequencies (with Flim1 = Flim2), distance between listening point and the engine, and finally by taking back some measurements such as oil housing, cylinder head, …. The second one concerned a comparison between 6 measured sounds with varying speed and varying distance of listening point, and one calculated sound. It appears clearly that the low number of measurement points needs to be compensated by an optimal choice of this points on elements that are the most important on real sound.
Elementary surfaces associated to this measurements, and limit frequencies for the two simplifications (dependent on length L and distance r) are also important to determine. In spite of the great complexity of this source, qualitative results (identification of motor speed) of this simplified approach are encouraging us to try it on other kind of structures before to go back on industrial complex devices.
3.2 Application on a simple vibrating structure
A vibrating panel coupled to a rigid parallelepipedic box is studied. The other faces of the box are thicker than the vibrating panel in order to radiate less than the chosen panel.
Vibratory measurements are taken at 12 points and acoustic predictions are compared to measured pressures at several points above the panel (see photo n°2).
Photo n°2 : the box with accelerometers and microphones in semi-anechoic field
Mechanical excitation is realised by two vibrating pots, hanged in the box and instrumented with force sensors (see photo n°3).
Photo n°3 : vibrating pots under the panel before closing
This experimental set up permits to apply two forces calibrated in time and frequency and can be therefore compared to an excitation of the cylinder head by a 2-cylinders engine. The supply of vibrating pots is realised by impulses with known characteristics, and determined repetitive frequency (see figure 1). Two parameters are used to design these signals. The first
one is the repetitive frequency of each channel that varies between 5Hz and 100Hz. The second one is the impulse width used to change the maximal excitation frequency (Fmax). Three kinds of excitations are used for measurements : low, medium and high frequencies limited respectively with Fmax to 200, 2000 and 20000 Hz.
Figure n°1 : Impulses generated by vibrating pots
For each impulse, forces are measured by force sensors for the 3 chosen values of Fmax : HF excitation has a clear cutting frequency at 10kHz, and level injected to the structure is very low compared to LF and MF excitation. Maximal level injected in the structure is very dependant on the frequency band imposed to the pots. Three different sound level can be obtained with these configurations, and quality of suggested simplifications can thus be evaluated.
3.2.1 Perceptive tests
The aim of these tests is to evaluate subjectively calculated sound compared to measured sounds with the same characteristics (kind of excitation and listening point).
For the first test (appariement forcé [S.McAdams ] see figure n°2), the listener has to match each sound to its reference. Results obtained with this test are easily readable.
Figure n° 2 : Graphical User Interface of test d’appariement forcé
Chosen characteristics must not lead to synthesised sounds too close or too far from each others. Indeed, the perceptive test must not take into account auditory quality of listeners and must not be a task too simplified. Listening point, for example, has not a great effect with this excitation because measured sounds at 4 different points are not really different. It is the same for excitation with too low or too high periodicity. Reference sounds base is composed of 9 sounds (1 to 9) with 3 repetition frequency (40Hz ,45Hz,50Hz), and 3 excitations (LF, MF, HF). Calculated sounds (A to I) have the same characteristics than reference sounds.
This test applied to 30 subjects give a recognizing ratio of 80% : subjects succeeded to find the main characteristics of sounds in calculated sounds. Fundamental frequency of impulse repetition is quite well recognized. Some inversions in close configurations are however possible. Configuration BF40 and BF45 and BF50 are hence sometimes confused between themselves but never with other configurations.
The second test (test d’appariement libre see figure n°3), analyse measured or mixed sounds with several sounds calculated with different synthetis method. The subject has to group sound by families according to a judgement criterion not defined.
Figure n° 3 : Graphical User Interface of test d’appariement libre
The analyse of results give some interesting information : the most important is the dissociation of LF sounds in this test. Record (measurements) and synthesis LF are placed on the same branch.
4 CONCLUSIONS
Suggested simplifications in time domain, already applied in frequency domain, are really interesting since they give the possibility to reduce greatly computation time and most of all they enable to realise an quick perceptive analyse leading to a sound hierarchy of sources in a noisy machine.
Subjective evaluation has been presented on a engine bench. Geometry complexity has shown the limits of the approach but also some interesting points to explore. Synthesised sounds for the box return reliably sounds at low frequency but some confusions can appear between medium and high frequencies. These confusions come from the few numbers of points since only 12 points are used to represent the vibratory field and to realise sound synthesis up to 12000Hz.
Finally, simplifications related to minimal listening distance are not really respected in experimental case because microphone are placed quite close to the vibrating surface to overcome the low sound level.
REFERENCES
[1] J. D. Chazot, “Synthèse d’un bruit moteur ” Rapport DEA : INSA Lyon LVA 2002.
[2] N. Hamzaoui, C. Boisson, “Calcul du rayonnement acoustique par une méthode intégrale simplifiée”, convention INRS n° 5951555-5951556, 1997.
[3] G. Guyader, “Modélisation temporelles simplifiées des phénomènes physiques à l’origine du bruit moteur dédiées au portage temps réel et aux applications de design sonore ”, Thèse de Doctorat 2003.
