A METHOD FOR THE INDIRECT MEASUREMENT OF ACOUSTIC POWER EMITTED BY SYNCRONOUS BELTS

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1 A METHOD FOR THE INDIRECT MEASUREMENT OF ACOUSTIC POWER EMITTED BY SYNCRONOUS BELTS A. Di Sante, G. Ferri*, G. M. Revel, G. L. Rossi Dipartimento di Meccanica Universita degli Studi di Ancona, Via Breece Bianche ANCONA, ITALIA *Dayco Europe SpA Via Gorizia, 52- Chieti Scala, IT ALIA ABSTRACT One of the main problems in direct measurement of synchronous belt noise is the considerable level of disturbing acoustic emission produced by other components of the transmission. This causes uncertainty when measuring the sound power specifically emitted by the belt. In recent years there have been only a few systematic studies on noise emission mechanisms and some noise causes have been identified. In this paper a method on how to investigate single noise causes is proposed. The methodology developed consists of two distinct phases. In the former, acoustic power emission is measured by means of acoustic intensity techniques. In the latter, an acoustic prediction is performed by using a Scanning Laser Doppler (SLDV) Vibrometer and data processing routines based on the superposition principle and on commercial Boundary Element codes. The SLDV is utilised for its non-intrusivity and capability of in-operation data measurement on the running belt. The results obtained in the two phases are compared to evaluate the influence of the vibratory behaviour on the total acoustic emission experimentally determined. NOMENCLATURE Ai : element of the vibrating source Si: emitting surface of Ai B : element of the acoustic grid (target) Vi :vibration velocity amplitude measured at point Ai <!Ji: vibration velocity phase measured at point Ai p: air density c: sound velocity in air ri: position vector of point B with respect to A; f : sound frequency w = 2 n f : angular frequency k= w I c : wave number p: sound pressure due to one element of the vibrating source BE: boundary element FE: finite element P 101 : sound pressure due to all the elements of the vibrating source PRMs: RMS value of Ptot I : acoustic intensity 1. INTRODUCTION Synchronous belts are generally considered low noise transmission systems with respect to others, such as chains or gears, but, particularly in the automotive industry, the need of very low acoustic emission levels stimulates research in this field. The main sources of noise generated by a transmission belt have been identified in [1], [2], [3], [4], [5]: -impact sound, which is generated by collision of tooth tip of wheel against bottom land of toothed belt at the beginning of the engagement; -sound due to transverse vibration of belt; -noise generated by the pulley vibration; -noise due to ejection of air between belt and pulley; -frictional noise. Nowadays, to our knowledge, no useful tool, correlation or experimental technique is available to estimate noise emission of a transmission belt once its operating conditions and geometrical characteristics are known. In this paper noise causes at meshing frequency are analysed. Firstly, the problem has been approached from the acoustical point of view. Two dedicated test benches have been set and acoustic intensity measurements have been performed. The main problem in directly measuring airborne belt noise is 1646

2 related to the fact that, in the application of interest, the belt is coupled to the engine and this generates many other types of noise that can mask the one under investigation [6]. This makes it difficult to employ measurement techniques based on microphones. A possible solution can be the indirect measurement of emitted sound power by vibration data processing [7], [8], [9], [1 0]. Therefore, in the second series of tests, vibration measurements have been performed on a belt using a Scanning Laser Doppler vibrometer (SLDV): This in order to develop an indirect measurement technique for single noise causes that can be used also in the practical case of a belt operating in a noisy environment. The aim of this technique should be the analysis of the correlation between the acoustical power emitted and belt parameters. 2. ANALYSIS OF AIRBORNE NOISE EMITTED FROM A BELT BY ACOUSTIC INTENSITY MEASUREMENT TECHNIQUES In order to improve understanding about noise generation in synchronous belts, two important phenomena have been analysed. The first is the resonant condition of the belt arm, while the second regards the noise and vibration generated at the meshing frequency under operational conditions. Therefore in the first series of tests, the acoustic emission of a stationary belt in resonance condition has been analysed by acoustic intensity measurement technique. A test rig has been built (see Fig. 1) with a belt transmission between an electric motor (variable speed motor able to reach 1400 rpm) and a camshaft of a cylinder head of an internal combustion engine. We designed this special set-up with the purpose of creating operating conditions closer to the real functioning of automotive timing belts. But it cannot be employed in the study of the acoustic emission while the belt is rotating, since the noise generated by the pump for the circulation of the lubricating oil would prevent any acoustic measurement. Anyway, it would be well suited for vibration measurements. In the experimental set-up a shaker put the belt in vibration at the resonance frequency of the belt arm. This particular condition allows to obtain a higher signal-to-noise ratio and then to validate the technique in ideal conditions. Belt tension was adjusted so as to obtain a resonance frequency of 94 Hz. In order to estimate the normal component of the intensity, acoustic measurements have been performed over a grid (35 measurement points) situated in front of the vibrating arm of the belt at 300 mm distance. Frequency analysis shows that the acoustic energy is mainly concentrated in the 1/3 octave band around 94Hz, as it was supposed to be. In correspondence of that frequency, we measured a sound power level of 68 db. A second test rig has been built (see Fig. 2) for the inoperation analysis disposing a two pulleys transmission and a driving electric motor able to reach 3000 rpm. This set-up allows variation of many parameters, such as type of pulleys and width of belt, and operating conditions, such as rotation velocity and belt tension. A rigid panel has been placed between the transmission and the electric motor, in order to create a baffle-wall. In order to speed up the execution of the large number of tests, acoustic intensity measurements have been performed using a scanning technique (ISO ). Instead of measuring the intensity vector point by point on a grid surrounding the emitting source, the acoustic power has been determined by continuos scanning of the acoustic probe (done manually) on a surface in front of the transmission. Preliminary tests performed by comparison with point by point measurement allowed to estimate a repeatability error smaller than 2 db for the case with continuos scanning. Preliminary tests have also shown the existence of a disturbing noise over the entire power spectrum due to the acoustic emission of the electric motor. Fig. 2- Test rig with a two pulleys transmission and a driving electric motor These problems led us to consider only the power level at the meshing frequency, as it was higher than anywhere else in the spectrum. In order to apply a validation criterion for the results, only the values which were 6 db higher than the emission due to the electric motor (running without the belt) at the same frequency were considered good and only if the

3 repeatability error between two measurements taken in the same test conditions was smaller than 2 db. A typical measured spectrum is shown in Fig.3. In the case investigated (rotation velocity of 1000 rpm, belt width of 35 mm, belt tension of 280N) an acoustic power of 61 db was found experimentally at the meshing frequency (787 Hz). This value has been achieved by subtracting the power measured with the motor running without the belt to the one measured with the belt. In this way the power value obtained should be related only to the belt. In conclusion the acoustic intensity technique allows to determine the global power emission of a running belt and its variation with operating and geometrical parameters. If the intensity is measured point by point over a grid, it becomes possible to obtain field maps and therefore to detect zones where emission is mainly concentrated [11]. But it is difficult, by using exclusively this technique, to assess which cause is predominant between the different mechanisms of noise generation. So we decided to try to obtain more information by vibration measurement trough laser techniques. the speckle noise induces a typical random uncertainty, while the second generates a systematic error, which is function of the measurement angle in the different positions. Belt Laser head Amplifier PC and controller Fig.4 - Experimental set-up for vibration velocity measurement on the stationary belt. [Hz] Fig.3 - Measured spectrum of acoustic power. 3. TRANSVERSAL VIBRATION MEASUREMENT ON THE BELT An initial session of vibration measurements has been performed on the test rig provided with the cylinder-head of an internal combustion engine. Measurements of transversal vibrations have been made by means of a Scanning Laser Doppler Vibrometer on the stationary belt excited by a shaker in the experimental set-up of Fig. 4. A second test session has been carried out on the test rig with the belt running (see Fig.2). The Laser Doppler technique allows to perform non contact measurements of transverse vibration on translating surfaces, but a considerable amount of noise and uncertainty can be due to the tangential velocity of the surface under test. This induces two main effects: the generation of speckle noise and, because of the non-orthogonality of the measurement direction to the surface, the addition of a part of the tangential component to the desired normal one in the results. These two interfering inputs have different nature: ~ ---- Laser head Video control / /' ~ Fig.5 Experimental set-up for vibration velocity measurement on the running belt. 1648

4 These effects can be reduced if the component of the tangential velocity along the incident laser beam is as small as possible. Therefore, the test rig has been placed horizontally and, in order to restrict the vibrometer scanning angle, the laser head has been positioned far from the belt. The drawback of this expedient is that, increasing the distance of the surface from the laser head, a reduction of the optical energy back to the vibrometer optics appears. Therefore a compromise must be found. In our case satisfactory results have been achieved by positioning the laser head at about 2 m distance from the belt arm. The measurement set-up is pictured in Fig. 5. The technique has been calibrated and validated using a triangulation sensor as reference. A typical measured spectrum is shown in Fig. 6. The peak at meshing frequency is clearly distinguishable at 787 Hz, suggesting a relation between arm vibration and noise emission at that frequency. A map of vibration velocity is illustrated in Fig. 7. This and similar vibration velocity distribution over the belt surface highlighted the fact that motion (and then acoustic emission) of the belt arm at meshing frequency is not concentrated near the pulley, but a standing wave exists on the whole belt arm between the two pulleys. 4. DATA PROCESSING BY SUPERPOSITION PRINCIPLE Amplitude and phase velocity data, measured by using the SLDV, can be employed to compute the acoustic field in front of the belt. This can be done using both measurement performed on a moving and vibrating or only vibrating belt. In this work, we decided to apply two different methods for the investigated cases, in order to have a validation for both of them. In the case of stationary belt, the elementary model based on the superposition principle [1 OJ, [12], [13] was applied. In this model we assume that the belt surface is composed by an array of simple sources; each source corresponds to the portion of area with centre in the vibration measurement point. In our experiments a grid of 35 points was used. The laser vibrometer allows to quickly resolve the vibration mode of the surface with high spatial resolution, this being necessary to describe the acoustic field with accuracy, particularly when velocity and phase of different points vary significantly. The acoustic pressure radiated by each element A; in a point 8 at a distance q (see. Fig. 8) is: p = Si (i p c k Vi I 2 n q) ei(wt- krr <Pi ). (1) Target surface 'i 25 E ~ ~.0 if :1! , Frequency (Hz] Fig.6- Measured spectrum of belt vibration. 10" 3!111~ frequency = 787Hz Source 80 so 40-0 Fig. 7- Vibration velocity distribution on the belt arm. Fig.8 - Scheme of the superposition principle The total pressure in 8 due to the whole belt arm vibration can be approximated by means of the superposition principle, i.e. by summing the contributions of all the elements. Clearly, for each couple of points of the measurement grid the phase difference must be considered. This phase difference has two components: the first is due to the difference of path length M i = rj'- q (2) 1649

5 which depends on geometry; the second is due to the different initial phases <Pi of the points of the moving surface: A laser scanning vibrometer allows to measure those phase differences if a reference signal for the subsequent acquisitions on the different points of the grid can be provided. In this case a proximity sensor was used. Once the contributions of each measurement point of the vibrating surface has been estimated, the total sound pressure in a point B of the acoustic field can be calculated by summing, at a given instant, each contribution (superposition principle): Then the RMS value of this expression PRMS can be calculated. The acoustic intensity on each point B of the target has been estimated using the expression: The total acoustic power has been thus evaluated by summing the products between intensity and areas over the whole grid. The value obtained at the resonance frequency was 69 db (see Table 1 ). (3) (5) The mesh represented both the transmission and the boundary between the fluid and the structure. The pulleys were assumed to be rigid, this because the values of the vibration velocities measured on them were negligible with respect to the belt ones. The FE model of the belt represented only the two arms of it, the two coiling zone were not taken into account, as they vibrate significantly only near the engagement zone for a few centimetres area. Each belt arm has been divided into a grid consisting of 4x1 0 mm 2 linear quadrilateral elements. The rigid panel placed between the transmission and the electric motor has been modelled as an acoustic symmetry plane. Because of the model nature (belt arms are open surfaces), the indirect boundary element formulation has been chosen [14]. Measured vibration velocities relative to the belt arms were the input data necessary to predict the acoustic radiation (the BEM code converts experimental data into velocity boundary conditions to be applied for acoustic field computation). Once the calculation is done, the BEM code allows to view the pressure or intensity distribution over any kind of surface defined and to calculate the acoustic power through it. We created a surface in front of the transmission quite similar to the one where experimental acoustic measurements were taken. The estimated acoustic power for the running belt at the meshing frequency (787Hz) is 58 db (see Table 1). 6. ANALYSIS OF RESULTS 5. DATA PROCESSING BY BEM CODES In the second case, when the belt is running and vibrating, the acoustic field has been calculated using BEM codes (SYSNOIS~,[14]). The numerical model consisted of a FE representation of the belt transmission (see Fig. 9) and a BE representation of the fluid. Finally, results predicted by the different methods (data processing by superposition principle and by BEM codes) have been compared with the experimental results obtained using the acoustic intensity technique. Results are summarised in Table 1. In the case of the stationary belt, the measured and predicted intensity distributions are shown in Fig It can be seen that they are quite similar. Also numerically, the agreement between the two kinds of data is good. In fact a difference of 1 db was found, as shown in Table 1. Anyway, it has to be said that this method is irrespective of reverberating phenomena, since it allows to predict only the acoustic emission of a vibrating surface in space. Also in the case of rotating belt, the comparison between predicted and measured power values is satisfactory (see Table 1 ), since the difference is 3 db. The higher value with respect to the first case is justified as follows. Firstly, the values obtained by BEM technique should be smaller than the measured ones, since the vibrations of coiling zones and pulleys have been neglected, as well as other hypothetical noise mechanisms. FREQUENCY SUPERPOSITION BEM INTENSITY METHOD MEASUREMENT 94 Hz (resonance) 69 db - 68dB 787 Hz (meshing) - 58 db 61 db Fig.9 -The FE representation of the belt transmission. Table 1 - Sound power values estimated using different techniques. 1650

6 db 68 db Fig Acoustic intensity maps for the stationary belt in resonance condition: calculated by superposition method (left) and measured (right). Furthermore the uncertainty in the velocity measurement may introduce some more discrepancies in the results. The predicted acoustic intensity map is shown in Fig. 11. It can be seen that the emission is mainly concentrated in front of the tensioned arm and in correspondence of the meshing zones of the two pulleys. A similar map was not carried out also experimentally because of the presence of other significant noise sources. The coherence of the results permits to assess the validity of both the proposed methods. Furthermore, in the case of rotating belt, we are allowed to conclude that most of the noise generated by a transmission belt at the meshing frequency is caused by the arm vibrations. Therefore other causes seem to be not so influent. This important conclusion would have not been possible, if only acoustic intensity measurements were used. The validity of both the methods has been assessed by comparison with experimental results achieved by acoustic intensity measurements. Differences in the order of 1 +3 db was found, which can be considered satisfactory. In addition, the comparison between experimental and predicted results allows to extract important information concerning the relevance of single noise causes. Future developments of this work will be a detailed uncertainty analysis for the velocity measurement and the predicted acoustic power. Furthermore, also the application of this tool to belts working on more complex test benches with loads and on real engines will be approached. REFERENCES 7. CONCLUSIONS In this work the problem of measuring the airborne noise emitted form a synchronous belt is approached by processing of experimental vibration data. A Scanning Laser Doppler Vibrometer was used for measurement, since, because of its non-intrusivity, it allows to perform the tests also under operational conditions, i.e. with the belt running. Two different methods are presented for calculation: the first is based on the superposition principle (Rayleigh integral), while in the second a Boundary Element code has been utilised [1] A. Kubo et al., "On the running noise of toothed belt drive ", Bulletin of JSME, Vol. 14, No 75, 1971, p [2] ibid., p.998. [3] M. Kagotani et al., "Some methods to reduce noise in toothed belt drives", Bulletin of JSME, Vol. 24, No 190, 1981, p.723. [4] T. Koyama et al., "A study on timing belt noise", Journal of Mechanical Design, Vol 112, Sept. 1990, p.419. [5] Y. Birembaut, M. Deschamps, "Etude des mecanismes de generation du bruit emis par les courroies crantees", Industrial Acoustics Department, Centre Technique des Industries Mecaniques (CETIM}. [6] P. Miranti, "Belt noise: descriptions, causes and remedies", Dayco Technical Center, 1974, n 5.

7 {m/s] Veloci11 B.C. 1nteml1v [Wim 2 ] 1.040E E E E E E D2E E+OI 5.202E E E E E E E E+02 Fig.11 -Acoustic intensity map obtained by BEM code at the meshing frequency. [7] ISO!TR 7849 «Estimation of airborne noise emitted by machinery using vibration measurement». [8] L. Bregant, P. Mas, P. Sas, «Vibration pattern analysis of sound radiating structures using laser vibrometer measurements», First iternational conference on Vibration Measurements by Laser Techniques, Ancona, Italy, 3-5 oct [9] D. E. Montgomery, R.L. West, R.A. Burdisso, H.E. Camargo, «Acoustic Radiation prediction of a compressor from 3D experimental spatial dynamics modelling», First iternational conference on Vibration Measurements by Laser Techniques, Ancona, Italy, 3-5 oct [1 OJ G.M. Revel, G.L. Rossi, "Sound power estimation by laser Doppler vibration measurement techniques", to be published in "Shock and Vibrations" [11] Y. Birembaut, J. Tourret, M. Deschamps, "Noise generation of synchronous belts using acoustic intensity mapping", Noise Control Engineering Journal, January- February, [12] P.M. Morse, K. U. lngrad, Theoretical Acoustics, Me Graw Hill, [13] L. E. Kinstler, A. R. Frey,. A. B. Coppens, J. V. Sanders, "Fundamentals of Acoustics", John Wiley & Sons, [14] Sysnoise "User's manual", LMS Numerical Integration Technologies, Leuven (Belgium). 1652