Noise source localization on washing machines by conformal array technique and near field acoustic holography

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1 Proceedings of the IMAC-XXVIII February 1 4, 2010, Jacksonville, Florida USA 2010 Society for Experimental Mechanics Inc. Noise source localization on washing machines by conformal array technique and near field acoustic holography Paolo Chiariotti a, Milena Martarelli a, Enrico Primo Tomasini a and Ravi Beniwal b a Department of Mechanical Engineering, Università Politecnica delle Marche, Via Brecce Bianche, Ancona, Italy b SenSound, 440 Burroughs St., Suite 170, Detroit, MI 48202, USA ABSTRACT The acoustic emission of a washing machine has been deeply studied by comparing three different techniques, which are: - conventional acoustic intensity, - planar near-field acoustic holography and conformal array technique based on the Helmotz Equations Least Squares method. These techniques have been used to measure the front of a washing machine, i.e. the more critical side from the acoustic comfort point of view in the working environment. The acoustic intensity measurement has been taken as reference for the comparison of the two other techniques. The sound intensity probe has been scanned over a grid of several discrete positions and the acoustic intensity and pressure on the measurement plane have been determined. For both the conformal and planar near-field acoustic holography techniques an antenna of 30 microphones has been employed scanning over several positions in order to cover the entire washing machine front with a spatial resolution of 2.5 cm (maximum frequency Hz). Advantages and limitations of the noise source location techniques have been examined thoroughly. 1. Introduction The home appliance market is very large world-wide; practically every family in any country is a customer of appliances. The washing machine represents a type of appliance which is rapidly embodying high level technology and is sold in million items per year in the world. Nowadays acoustic comfort is becoming a key objective of washing machine manufacturers, thus it is necessary to accurately locate main noise sources. A washing machine is an electromechanical system, basically composed of a metal cabinet which hosts internally a tub which in turn contains the rotating drum, driven by an electric motor, in most cases through a pulley and with a control board which manages the washing cycles. Because of such a structure both noise sources coming directly from the drive system and those produced by the external cabinet mode shapes have to be expected. Water in the tub also produces the classical splash noise which can be annoying especially for long washing programs. Understanding the spatial distribution of noise sources on washing machine thus becomes an attractive challenge for acoustic measurement techniques. Standard measurements on such appliances are usually performed through the use of sound intensity probes: in this paper advanced array techniques like Near field Acoustic Holography (NAH) and Helmotz Equation Least Square (HELS) have been used to precisely identify noise sources on the front side of a standard washing machine, while intensity probe measurements have been performed in order to compare results with a classical technique. For the first time NAH and HELS have been applied to a real test case such as a running washing machine. Up to now the performances of the two techniques have been compared only on laboratory test cases, [1]. 2. Basic theory review 2.1. Sound intensity measurements The usefulness of measuring sound intensity is directly related to its vectorial nature. This allows testing to overcome problems coming from standard pressure measurements, which are often misleading if not performed

2 in controlled environments (e.g. anechoic rooms). The knowledge of both the amplitude and the direction of an acoustic field allows testing to locate the sources of sound. The most used method of measuring sound intensity in air is the two microphone (or p-p probe) method. This approach uses two closely spaced and phase-matched microphones and relies on the finite difference approximation to the sound pressure gradient. The distance between microphones define the measurable frequency range. Several configurations are possible: (i) measurement at discrete points or, (ii) measurement by continuously scanning the measurement plane with the sound intensity probe. If it can be defined an hypothetical surface that completely encloses the noise source (in conjunction with an acoustically rigid and continuous surface, i.e. if the source lies on the floor), the sound intensity measurement on this surface can be used to determine the sound power level of the source itself (according to the standard 9614-Part 1 for measurement at discrete points and 9614-Part 3 for scanning measurement [2,3]). From sound intensity measurements the acoustic quantities such as pressure, active and reactive intensity and power can be calculated Near Field Acoustic Holography Near Field Acoustic Holography (NAH) is an efficient method for the determination of the acoustic field generated by a noise source on the 3D space surrounding the source itself. The technique is based on near field measurement via microphones array. From the acoustic pressure data measured on the array surface (the hologram) 3D acoustic field can be reconstructed, with high spatial resolution, depending on the spatial resolution of the array. The NAH basic assumption [4] is that the sound field can be described as a combination of planar and evanescent waves (with amplitude decreasing with the distance from the source). These latter have amplitude and direction represented by their wavenumber k (kx,ky,k z) defined along a generic direction as the ratio between the frequency and the propagation speed. The plane waves represent the sound field portion that propagates to the far field, while the evanescent waves describe the complex sound field which exist close to the emitting surface and is damped out in the far field. A particular application of NAH is the planar NAH where the measurement surface, i.e. the microphones array, is planar. From the sound pressure data p(rm,t), measured in the near field by the planar array, i.e. at the distance rm from the emitting surface, the sound field can be reconstructed at any plane parallel to the measurement one. The total 3D acoustic field p(r,t) can be determined at arbitrary distance r from the surface radiating the noise. One implementation of the planar NAH is the The Spatial Transformation of Sound Fields (STSF) technique developed at Brüel& Kjær [5,6]. The STSF is based on the measurement of the pressure cross-spectra over a planar surface close to the source. The acoustic field can be reconstructed at any plane parallel to the measurement one by performing a convolution of the pressure cross-spectra with a known Greem function ( e j(r rm ) k 2 k x2 k y2 4π r rm ). The power of this technique on reconstructing the acoustic field and the particle velocity directly on the radiating surface has been demonstrated in several applications, like [7]. In particular, measurement of high spatial dense surface vibration velocity performed via scanning laser Doppler vibrometry has been used to validate the particle velocity calculated via STSF on the emitting surface Helmotz Equation Least Square In this paper the results of the Helmholtz Equation Least Squares (HELS) method implemented by SenSound Acoustic Imaging are reported, [8,9]. HELS is based on the measurement of the sound using a conformal array (i.e. reproducing the shape of the radiating surface) placed near the surface itself, Figure 1 (a). The measured sound field is then curve-fitted using spherical wave functions, Figure 1 (b), this allows the visualization of pressure, intensity and velocity on the emitting surface, Figure 1 (c). Mathematically, HELS can be written as J p( r, f ) C j ( f ) j (r, f ) (1) j 1 where the expansion functions j are the particular solutions to the Helmholtz equation, at any distance r from the surface. The expansion coefficients Cj can be determined by requiring the assumed-form solution to satisfy the boundary condition at the measurement points, distant rm from the emitting surface:

3 J (2) p ( rm, f ) C j ( f ) j ( rm, f ) j 1 Vibrating object (a) (b) Figure 1 HELS process Therefore the expansion coefficients are determined by matching the assumed-form solution j to the measured data. Finally the errors in this approximation are minimized and optimized using the least squares method. Once the expansion coefficients are determined, the acoustic pressures anywhere in the space and on the source surface can be reconstructed. One unique feature of the HELS method is that reconstruction of the radiated acoustic pressure is not based on spatial sampling, but on synthesis of spheroidal functions. For example, if the source radiates a pure dipole sound, then theoretically reconstruction can be done exactly with no more than four expansion terms or equivalently, four measurements regardless the frequency. For an arbitrarily vibrating structure, the radiated acoustic pressure may be quite complex. Nevertheless, this acoustic pressure field can be expressed as a multipole expansion. Moreover, at low-to-mid frequencies the major contributions are from the first few expansion functions. The higher-order terms represent the small-scale effects and can be neglected. 3. Measurement set up The measurement object is a washing machine of principal dimensions sketched in Figure 2, together with the reference axis system. The front panel has been measured via sound intensity probe, STSF and HELS. The washing machine was driven at a constant rate of 1200 rpm (electric motor drive revolutionary rate, 20 Hz) in order to obtain a steady state excitation condition. y x Figure 2 Washing machine sketch

4 3.1. Sound intensity measurement set-up Sound intensity measurements have been performed through B&K 3595 p-p probe. A scanning grid of 0.70m 0.98m (x and y direction respectively) with 10 rows and 14 columns was chosen to locate noise sources 2 on washing machine, see Figure 3. Segments of m have thus been used to calculate sound power over the measurement area. The scanning grid was placed m far away from the front panel of the washing machine. A time acquisition of 30s was chosen to evaluate sound intensity on each measurement segment. Scan direction Scanning Grid: Number of Rows=10; Number of Columns=14; Segment Area=0.07m 0.07m= m 2; Grid Area=0.70m 0.98m; Measuring distance=0.250m; Acquisition time (T)=30s. y x Figure 3 Sound intensity measurement and acquisition parameters 3.2. STSF measurement set-up STSF measurements have been performed through B&K 7688 system. All measurements have been performed using an array of 30 microphones (B&K 4935) placed at m from the front panel and automatically moved through a Cartesian X-Y moving robot, see Figure 4, and a set of 6 reference microphones fixed at several positions around the washing machine. (c) (a) (b) Figure 4 STSF microphones array fixed on the Cartesian X-Y moving robot (a) placed in front of the washing machine (b) and scanning positions (c) Several interlaced positions (4x4) have been acquired, see Figure 4(c), in order to have the possibility of covering an area bigger than the frontal surface of the washing machine and of calculating the sound field at sufficient low frequency range. The interlacing allowed to increase the spatial resolution of the microphones from m (real distance between microphones) to m in order to increase also the high frequency range for the sound field calculation.

5 Six reference microphones have been used to perform a Principal Component Analysis (PCA) once all scan had been acquired. This procedure enables the end user to separate correlated and uncorrelated sources during postprocessing phase. bearing motor pump Rear right side front Figure 5 Reference microphones positions 3.3. HELS measurement set-up The HELS measurement has been performed with an array of 6x5 microphones, see Figure 6, that was moved over the washing machine front panel in order to reproduce a sufficient conformal measurement surface. The measured patches (6x5) are shown in Figure 7. The blue meshes correspond to the microphones array s positions and the light blue mesh represents the calculation positions, i.e. located on the washing machine front panel surface. In order to process the patches all together, since they have been measured at different time instants, a reference microphone has been used to realign them in time. The microphones arrays distance from the washing machine surface was of about m.

6 Reference microphone Figure 6 Microphones array and reference microphone 4. Discussion of results Figure 7 Microphones arrays positions (blue patches). The sound intensity maps measured by the sound intensity probe at m from surface have been compared with the maps calculated by the STSF in the far field at m from the measurement plane, it being located at m from the emitting surface. In Figure 8 two maps at 400 Hz and 1600 Hz are given, the latter being the

7 frequency at higher emission around the tub area. The sound intensity level and distribution calculated by the STSF system is equal to the intensity measured by the intensity probe, with an improvement on spatial accuracy due to the large number of measurement microphones. db (db ref 10pW/m 2 ) 400 1/3 octave band Hz banwidth /3 octave band Hz banwidth Figure 8 Intensity maps at m from the washing machine front panel. The results of the two holographic systems have been compared in terms of Sound Pressure Level (SPL) and air particle velocity calculated on the emitting surface, the washing machine front panel. Figure 9 shows the comparison between the SPL distribution for three frequencies: - at 800 Hz the maximum pressure is radiated by the soap drawer, - at 1200 Hz the noise amplification due to the reflection from the floor is evident, - at 1600 Hz the emission from the porthole is clear. Figure 10 gives the air particle velocity distribution and the active intensity over the washing machine front panel at the most interesting frequency, i.e. at 1600 Hz where the maximum emission is located on the basket aperture. 5. Conclusions Two kind of near field acoustic holography, the planar one based on Spatial Transformation of Sound Fields (STSF) and the spherical one based on conformal array measurements and Helmotz equation least-square method (HELS) have been applied for the first time to a real test case and their results compared. The location of the noise source is very accurate with both the techniques either in terms of SPL, sound intensity and air particle velocity. For an almost planar test case, as it is the washing machine front panel, the test implementation (array microphone preparation, noise source geometry definition) is very simple in the case of STSF, and more complex for the HELS system, however, that complexity is indispensable for 3D objects where conformal arrays are necessary and planar holography is not appropriate. The results of the STSF have been validated also by means of a traditional scanning technique based on sound intensity measurements with a p-p probe following the international standards for noise source location.

8 db (db ref 20 Pa) 876 Hz Hz banwidth 1196 Hz Hz banwidth 1600 Hz Hz banwidth Figure 9 SPL maps on the washing machine front panel.

9 1600 Hz (m/s) Hz banwidth (db) Air particle velocity 1600 Hz (W/m 2 ) Hz banwidth (db) Active intensity Figure 10 Air particle velocity maps on the washing machine front panel. References [1] J. Gomes, F. Jacobsenn, M. Bach-Andersen, Statistically optimised near field acoustic holography and the Helmholtz equation least squares method: a comparison [2] ISO :1993 Acoustics-Determination of sound power levels of noise sources using sound intensity-part1: Measurement at discrete points. [3] ISO :1993 Acoustics-Determination of sound power levels of noise sources using sound intensity-part2: Measurement by scanning. [4] J. D. Maynard, E. G. Williams, and Y. Lee, Near-field acoustic holography. I: Theory of generalized holography and the development of NAH, J. Acoustical Society of America 78 (4), , 1985; [5] J. Hald and K. B. Ginn, Spatial Transformation of Sound Fields: principle, instrumentation and applications, Proceedings of the Acoustic Intensity Symposium, Tokyo, 1987; [6] Spatial Transformation of Sound Fields Software Type 7688 User Manual, Brüel & Kjær; [7] M. Martarelli, G. M. Revel, E. P. Tomasini, Laser Doppler Vibrometry and Near-Field Acoustic Holography: different approaches for surface velocity distribution measurements, Fifth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, SPIE, 4827, Ancona, 2002; [8] Z. Wang, S. F. Wu, Helmotz equation-least squares method for reconstructing the acoustic pressure field, J. Acoustical Society of America 102 (4), , [9] S. F. Wu, Methods for reconstructing acoustic quantities based on acoustic pressure measurements, J. Acoustical Society of America 124 (5), , 2008.